Oh, I have some here. I wonder if I can help you. If the landlord is good, he should get extra points!

1. The minimum multiple of a number is itself, and there is no maximum multiple.

2. The multiple of a number is infinite.

3. The smallest factor is 1, and the biggest factor is itself.

4. The number of factors of a number is limited.

5. To find a multiple of 5, just find a number with a bit of 5 or 0.

6. Find a multiple of 2 and find a number of 2, 4, 6, 8 and 0.

A multiple of 7.2 is called an even number, and a multiple of 2 is not called an odd number.

If it is a multiple of 3, then the sum of its digits must be a multiple of 3.

9. There are only two factors, 1 and itself. Such numbers are called prime numbers or prime numbers.

10. Besides 1 and itself, there are other factors. Such numbers are called composite numbers.

I extracted this from the book. I wonder if I can help you?

Don't copy from downstairs. Please pay attention to it for me.

2. What is the concept of primary school factor?

In primary school mathematics, two positive integers are multiplied, so both numbers are called factors of product, or divisors.

Definition of primary school mathematics: If a*b=c(a, B and C are integers), then we call A and B factors of C. ..

For example, 2*3=6. At this time, we can say that 2 and 3 are factors of 6.

The definition of primary school mathematics mentioned above is based on the fact that abc is an integer. If abc is all fractions or other numbers, it is impossible to say who is the factor of who and who is the multiple of who at this time.

Some people may ask, what about 0? Primary schools don't consider 0, because primary school students' thinking is still relatively simple, and they can't understand such complicated content for the time being. Therefore, the knowledge related to the factors that primary schools are exposed to is relatively simple and easy to understand.

Extended data:

In fact, factors are generally defined as integers: let a be an integer and b be a non-zero integer. If there is an integer Q that makes A=QB, then B is a factor of A, denoted as B | A ... but some authors do not require B≠0.

For example, in the formula 3*8=24, we can see that the product of 3 and 8 is 24. At this time, we say that 3 and 8 are factors of 24. 24 is a multiple of 3 and also a multiple of 8. 24 is eight times that of 3 and three times that of 8.

References:

Sogou encyclopedia-factor

3. Information about factors and multiples

I. Factor data

1, definition of factor:

Multiply two positive integers, then both numbers are called factors of product.

Factors are also called divisors. If the integer n is divided by m, the result is an integer with no remainder, then we call m a factor of n. It should be noted that this relationship only holds if the dividend, divisor and quotient are integers and the remainder is zero. On the contrary, we call n a multiple of m, such as 2X6= 12. The product of 2 and 6 is 12, so 2 and 6 are factors of 12.

2. Examples of factors:

The factors of 6 are: 1 and 6, 2 and 3.

The factors of 9 are: 1 and 9,3.

The factors of 10 are: 1 and10,2 and 5.

The factors of 15 are: 1 and15,3 and 5.

3, factor knowledge expansion:

Definition of common factor: The common factor of two or more integers is called their common factor.

The greatest common factor of two or more integers is called their greatest common factor.

Inference: 1 is the common factor of any number of integers.

Between two nonzero natural numbers with multiple relationships, the smaller number is the greatest common factor of these two numbers.

Second, multiple data:

1, the definition of multiple: ① An integer can be divisible by another integer, and this integer is a multiple of another integer. For example, 15 can be divisible by 3 or 5, so 15 is a multiple of 3 and 5. (2) The quotient obtained by dividing one number by another. For example, a÷b=c, that is, A is a multiple of B. If a number is divisible by its product, then it is a factor, and its product is a multiple. 3 * 5 = 15 。 Factor 1 multiple of factor 2, for example: A÷B=C, it can be said that A is c times of B. (3) A number has countless multiples, that is, * * * of a multiple of a number is an infinite set. Note: you can't call a number a multiple alone, you can only say who is a multiple of who.

2. Examples of multiples:

A multiple of 2

At the end of a number is an even number (0, 2, 4, 6, 8), which is a multiple of 2.

Like 3776. The end of 3776 is 6, which is a multiple of 2. 3776÷2= 1888

Multiple of 3

The sum of the digits of a number is a multiple of 3, and this number is a multiple of 3.

4926。 (4+9+2+6)÷3=7, which is a multiple of 3. 4926÷3= 1642

3. Multiple knowledge expansion:

The square difference of any two odd numbers is a multiple of 8.

Prove: Let any odd number 2n+ 1, 2m+ 1, (m, n∈N).

(2m+ 1)^2-(2n+ 1)^2

=(2m+ 1+2n+ 1)*(2m-2n)

=4(m+n+ 1)(m-n)

When both m and n are odd or even, m-n is even and divisible by 2.

When m and n are odd and even, m+n+ 1 is even and divisible by 2.

So (m+n+ 1)(m-n) is a multiple of 2.

Then 4(m+n+ 1)(m-n) must be a multiple of 8.

4. Detailed knowledge of factors and multiples in the first volume of the fifth grade

Knowledge points:

1, know natural numbers and integers, and know multiples and factors related to multiplication.

Numbers like 0, 1, 2, 3, 4, 5, 6, … are natural numbers.

Numbers like -3, -2,-1, 0, 1, 2, 3, ... are all integers.

2. We only study multiples and factors within the range of natural numbers (except zero).

3. Multiplication and factor are interdependent. Make it clear who is the multiplier and who is the factor.

Supplementary knowledge points:

The multiple of a number is infinite.

Multiplicity characteristics of exploration activity (1) 2,5

Knowledge points:

1 and multiples of 2.

Numbers in units of 0, 2, 4, 6 and 8 are multiples of 2.

Characteristics of multiples of 2 and 5.

A number with 0 or 5 is a multiple of 5.

3. Definition of even and odd numbers.

Numbers that are multiples of 2 are called even numbers, and numbers that are not multiples of 2 are called odd numbers.

4. You can judge whether a number is a multiple of 2 or a multiple of 5. It can be judged whether a non-zero natural number is odd or even.

Supplementary knowledge points:

It is a multiple of 2 and a multiple of 5. A number with a unit of 0 is a multiple of both 2 and 5.

Multiplicity characteristics of exploration activity (2)3

Knowledge points:

1 and multiples of 3.

The sum of the digits of a number is a multiple of 3, and this number is a multiple of 3.

2. You can judge whether a number is a multiple of 3.

Supplementary knowledge points:

1, which is a multiple of 2 and 3.

The number of each digit is 0, 2, 4, 6, 8, and the sum of each digit is a multiple of 3, which is both a multiple of 2 and a multiple of 3.

It is a multiple of 3 and 5 at the same time.

The number on each digit is 0 or 5, and the sum of numbers on each digit is a multiple of 3, which is both a multiple of 3 and a multiple of 5.

3. It is a multiple of 2, 3 and 5 at the same time.

The number of one digit is 0, and the sum of the numbers of each digit is a multiple of 3, which is not only a multiple of 2 and 5, but also a multiple of 3.

Find a factor

Knowledge points:

Find all the factors of a natural number from 1 to 100. Methods: Use the multiplication formula to think about which two numbers are multiplied to equal this natural number.

Supplementary knowledge points:

The number of factors of a number is limited. The smallest factor is 1, and the biggest factor is itself.

Looking for prime numbers

Knowledge points:

1, understand the meaning of prime numbers and composite numbers.

A number has only two factors, 1 and itself. This number is called prime number.

A number has other factors besides 1 and itself. This number is called a composite number.

2. 1 is neither prime nor composite.

3. Judge whether a number is a prime number or a composite number:

Generally speaking, first of all, we can judge whether this number has factors 2, 5 and 3 by "the characteristics of multiples of 2, 5 and 3"; If you can't judge yet, you can try to divide by smaller prime numbers such as 7, 1 1 to see if there is a factor of 7, 1 1. As long as we find a factor other than 1 and itself, we can determine that this number is a composite number. If no other factor can be found except 1 and itself, this number is a prime number.

Equal number of people

Knowledge points:

1, using the methods of "list" and "drawing schematic diagram" to find the law;

The ship was originally on the south bank, sailing from the south bank to the north bank, and then sailing back from the north bank to the south bank, constantly going back and forth. Through the methods of "list" and "sketch", we will find the law of "odd times on the north bank and even times on the south bank"

2. Be able to use the parity of the numbers found above to solve some simple problems in life.

3. Through calculation, the law of parity change is found:

Even+even = even odd+odd = even.

Even+odd = odd

5. Five factors and multiple stories

1. Group game: put a cup mouth up on the table, turn it right 1 time, turn it down twice, turn it left three times ... Think about it: if the mouth is up, how many times did it turn over? Students do experiments and fill in the table below.

Fill in the form: for the first time, the second time, the third time and the fourth time, the cup mouth is upward ... The reaction number is 48 12 16 ... The formula is 4 *1= 44 * 2 = 84 * 3 =124 * 4. Show: Because 4*2=8, 4 is a factor of 8, and 2 is also a factor of 8; 8 is a multiple of 4 and 8 is also a multiple of 2.

Try to say: ● Because 4*3= 12, so …● Because 4*4= 16, so …… Teacher: Do you want to modify it? Just four sentences, now how to become two sentences? ● Because 4* 1=4, so ... Teacher: Do you understand the relationship between factor and multiple? Can you write a formula to test your deskmate? Students write formulas. Teacher: Who will work out a formula to test the class? 1:50*2= 100.

Health 2:25*25=625. Teacher: Miss Gao also wants to write a formula.

(Blackboard: 24÷3=8) Can you tell me who is a factor and who is a multiple? A lifetime answer. Teacher: We can know the factor and multiple not only by multiplication formula, but also by division formula.

Teacher: Today we will learn more about factors and multiples. (Exhibition topic: Multiplicity factor) III. Research Multiplicity 1. Teacher: What are the characteristics of these numbers in the game just now? (blackboard writing: multiple of 4) What is the multiple of 4? (Blackboard: 4,8, 12, 16) Teacher: Are these numbers multiples of 4? (Blackboard: 24, 28, 32) Teacher: When will Miss Gao finish it? Health: I can't finish it.

Teacher: What can I say if I can't finish my math? Health 1: infinite. Health 2: Countless.

Teacher: What symbol can be used to represent it? Health: ellipsis. Teacher: What are the characteristics of these figures? (Integer) What other numbers are multiples of 4? Health: For example, 4.4 and 8.8 are also multiples of 4.

Teacher: When we study multiples and factors, we usually refer to (display: a natural number that is not 0) Teacher: Is there any good way to find multiples? Health 1: Just add 4 each time. Teacher: Did you find a multiple of 5 and increase it by 4 each time? Health: No, it increases by 5 every time.

Health 2: I found that it is a regular multiplication. For multiples of 5, multiply 5 by 1, 5 * 2, 5 * 3...2. Try it: ① Please find multiples of 3.

Who can quickly find the multiple of 9 within 50? Teacher: Can you find the multiple of 3 in this way? According to the students' answers on the blackboard: 3, 6, 9, 12, 15, 18...3. Can you find out the characteristics of multiples? The number of multiple factors has countless maxima and minima. 4. Judge that the minimum multiple of ① 17 is 84. ②6 is a multiple of 2 and 3.

Teacher: Can you imitate this sentence and say a word? 36 is a multiple. Teacher: It seems that it is not enough to study multiples alone, but also-factors.

Fourth, study the factor and find out the factor of 12 by your own method. Please give four performances.

Health 1: 1,12; 2,6; 3,4。 Health 2:6, 2; 3,4; 12, 1。

Health 3: 12, 6, 4, 3, 2, 1. Health 4: 1,12; 2,6; 3,4。

Teacher: Which student do you think writes better? Health: I like the fourth one because it is written in groups. The teacher hits the stars.

Teacher: What do you think of the third one? Health: Not good. Teacher: I want to shout a foul for the third classmate. The division of teachers is also very good

Teacher: Now, can you find a numerical factor? Health: Yes. Teacher: Then please write down the factor of 16.

Teacher: Discussion: What's the difference between factor and multiple? Blackboard: Multiple factors have infinite finite maximums, and its own minimum is 1. Fifth, practice-think about doing the fourth question. The factor of 9 from small to large is _ _ _ _ 6 times of 9, which is _ _ _10, and from small to large is _ _ _10, which is _ _ _ _ 6, respectively.

When the turntable rotates, the pointer points to the number when it stops. Ask the students to tell the relationship between 8 and multiples of this number. Teacher: It's not enough to play like this. Let's play another game. Dare to accept the game? Rule: If the number is a multiple of 8, the teacher and I will win; If you turn to a factor of 8, you win.

Life is strong * * *: We are not cost-effective! Health: We only have three factors of 8 and five multiples of 8. Teacher: You can design this situation yourself.

Please design your own number. No matter how you turn it, you win. With today's knowledge, the numbers cannot be repeated.

Organize students to design their own turntables. The middle number given by the teacher is 36. Requirements: Students must be guaranteed to win every game. Given the median number of 24, it is required to ensure that the teacher wins every game.

Given the median number 10, teachers and students are required to have as many opportunities as possible to win each competition result.

6. What is a factor and what is a multiple?

definition

An integer can be divisible by another integer, which is a factor of the former.

Example: 6÷2=3 2 and 3 are factors of 6.

classify

In division A, if the dividend is divided by the divisor, the quotient obtained is a natural number, and there is no remainder, it is said that the dividend is a multiple of the dividend, and the divisor and quotient are factors of the dividend.

B We divide a composite number into several prime numbers, which are called prime factors of this composite number.

Factors and factors

There are three differences between divisors and factors:

1, the number fields are different. The divisor can only be a natural number and the factor can be any number.

2. The relationship is different. Divider refers to the divisible relationship between two natural numbers. As long as two numbers are natural numbers, it can be determined whether there is a divisor relationship between them, such as: 40÷5=8, 40 is divisible by 5, 5 is the divisor of 40,12 ÷10 =1.2,655438. A factor is the relationship between two or more numbers and their products. For example, 8*2= 16, 8 and 2 are all factors of the product 16, and there is no factor without the product formula.

3. The relationship between size is different. When the number A is a divisor of the number B, A cannot be greater than B, and when A is a factor of B, A can be greater than B or less than B. ..

Generally speaking, divisor equals factor.

common factor

Definition: The common factor of two or more natural numbers is called their common factor.

Greatest common factor: the greatest factor of two numbers.

Other: 1 is the common factor of all nonzero natural numbers.

Between two natural numbers with multiple relationships, the smallest number is the greatest common factor of these two numbers.

correlation factor

1) The minimum factor of a natural number is 1, and the maximum factor is itself.

2) 1 is the common factor of all nonzero natural numbers.

An integer can be divisible by another integer, which is a multiple of another integer. For example, 15 can be divisible by 3 or 5, so 15 is a multiple of 3 and 5. (2) The quotient obtained by dividing one number by another. For example, a÷b=c, that is, A is C times of B and A is a multiple of B. If a number is divisible by its product, then it is a factor and its product is a multiple. 3 * 5 = 15 ↑ ↑ ↑ factor 65438+ multiple of factor 2, for example: A÷B=C, it can be said that A is c times of B, and a number has countless multiples, that is, * * * of a multiple of a number is an infinite set. Note: you can't call a number a multiple alone, you can only say who is a multiple of who.

7. Five little knowledge of primary school mathematics

Commonly used quantitative relationships are 1, number of shares * number of shares = total number of shares ÷ number of shares = number of times of 2,65438 per share +0 * multiple = multiple of 65438+multiple of 0 = multiple of 65438+multiple of 0 = multiple of 65438+multiple of 0 = 3. Quantity = total price ÷ total price ÷ unit price = total price ÷ quantity = unit price 5, working efficiency * working time = total work ÷ working efficiency = working time ÷ total work = working efficiency 6, addend+addend = sum- one addend = another addend 7, minuend-minuend = difference. Divider ÷ Divider = quotient dividend ÷ quotient = divisor quotient * Divider = divider calculation formula for primary school mathematical figures 1, square (c: perimeter s: area a: side length) perimeter = side length *4 C=4a area = side length * side length S=a*a 2, cube (3). Area = length * width S=ab 4 height V=abh 5, triangle (s: area a: bottom h: height) area = bottom * height ÷2 s=ah÷2 triangle height = area *2÷ bottom triangle bottom = area *2÷ height 6, parallelogram (s:. Height ÷2 s=(a+b)* h÷28, circle (s: area c: perimeter л d= diameter r= radius) (1) perimeter = diameter *л=2*л* radius c = л. Height =ch(2лr or лd) (2) surface area = lateral area+bottom area *2 (3) volume = bottom area * height (4) volume = lateral area ÷2* radius 10, cone (v: volume h: height s: bottom area r). The formula of sum difference problem: (sum+difference) ÷2= large number (sum-difference) ÷2= decimal 13, and the problem of multiple: sum ÷ (multiple-1)= decimal * multiple = large number (or sum-decimal = large number). Meet time = meet distance ÷ speed and; Speed sum = meeting distance ÷ meeting time 16, concentration problem Solute weight+solvent weight = solution weight * 100%= concentration solution weight * concentration = solute weight ÷ concentration = solution weight 17, profit and discount problem. Profit rate = profit/cost * 100%= (selling price/cost-1)* 100% fluctuation amount = principal * fluctuation percentage; Interest = principal * interest rate * time; After-tax interest = principal * interest rate * time * (1-20%) common unit conversion length unit conversion 1 km =1000m1m =1decimeter1decimeter =/kloc. = 100 ha 1 ha = 10000 m2 1 m2 = 100 cm2 1 cm2 = 1 00 mm2. Kloc-0/ kg = 1 kg RMB unit conversion: 1 yuan = 10 angle 1 0 minute 1 yuan = 100 minute time unit conversion:. \3\5\7\8\ 10\ 12 Abortion (30 days) is: 4\6\9\ 1 1 February 28th in a flat year, February 29th in a leap year, and June 30th in a flat year. Leap year 366 days 1 day =24 hours 1 hour =60 minutes 1 minute =60 seconds 1 hour = 3,600 seconds Basic concepts Chapter I Calculation of Numbers and Numbers A concept (I) Integer 1 Meaning: sum of natural numbers.

2 natural numbers: when we count objects, 1, 2, 3 ... the numbers used to represent the number of objects are called natural numbers. There is no object, which is represented by 0.

0 is also a natural number. Counting units one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.

The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.

4 digits: Counting units are arranged in a certain order, and their positions are called digits. The divisible integer A of the number 5 is divisible by the integer B (b ≠ 0), and the divisible quotient is an integer with no remainder, so we say that A can be divisible by B, or that B can be divisible by A. ..

If the number A is divisible by the number B (b ≠ 0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.

Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35. The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself.

For example, the divisor of 10 is 1, 2,5, 10, where the smallest divisor is 1 0 and the largest divisor is 10. The number of multiples of a number is infinite, and the smallest multiple is itself.

The multiple of 3 is: 3, 6, 9, 12 ... The minimum multiple is 3, but there is no maximum multiple. Numbers in units of 0, 2, 4, 6 and 8 can be divisible by 2, for example, 202, 480 and 304 can be divisible by 2.

Numbers in units of 0 or 5 can be divisible by 5, for example, 5,30,405 can be divisible by 5.

The sum of the numbers in each bit of a number can be divisible by 3, so this number can be divisible by 3. For example, 12,108,204 can all be divisible by 3.

The sum of each digit of a number can be divisible by 9, and so can this number. A number divisible by 3 may not be divisible by 9, but a number divisible by 9 must be divisible by 3.

The last two digits of a number can be divisible by 4 (or 25), and this number can also be divisible by 4 (or 25). For example,16,404 and 1256 can all be divisible by 4, and 50,325,500 and 1675 can all be divisible by 25.

The last three digits of a number can be divisible by 8 (or 125), and this number can also be divisible by 8 (or 125).