Children's education has always been a top priority for parents. All parents want their children to receive the best education and have a better future. To this end, I will provide you with important knowledge points of junior high school mathematics. I hope it will help parents and primary school students!

An Important Knowledge Point in Xiaoshengchu Mathematics: Integer

Numbers and digital operations

A concept

(1) integer

The meaning of 1. integer

Natural numbers and 0 are integers.

2. Natural numbers

When we count objects, 1, 2, 3 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.

3. Counting units: one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million and 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. Numbers

Counting units are arranged in a certain order, and their positions are called numbers.

5. Divisibility of numbers

When the integer A is divided by the integer b(b 0), the quotient is an integer with no remainder, so we say that A is divisible by B, or that B is 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, where the minimum multiple is 3 and 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). For example,1168,4600,5000, 12344 can all be divisible by 8, and 1 125,13375,5000 can all be/kloc-.

A number divisible by 2 is called an even number.

Numbers that are not divisible by 2 are called odd numbers.

0 is also an even number. Natural numbers can be divided into odd and even numbers according to their divisibility by 2.

A number with only two divisors of 1 is called a prime number (or prime number), and the prime numbers within 100 are: 2, 3, 5, 7,1,13, 17.

If a number has other divisors besides 1 and itself, then it is called a composite number. For example, 4, 6, 8, 9 and 12 are all complex numbers.

1 is not a prime number or a composite number, and natural numbers are either prime numbers or composite numbers except 1. If natural numbers are classified according to the number of their divisors, they can be divided into prime numbers, composite numbers and 1.

Every composite number can be written as the product of several prime numbers. Every prime number is a factor of this composite number, which is called the prime factor of this composite number. For example, 15=35, and 3 and 5 are called prime factors of 15.

Multiplying a composite number by a prime factor is called prime factor decomposition.

For example, decompose 28 into prime factors.

The common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor of these numbers. For example, the divisor of 12 is 1, 2, 3, 4, 6,12; The divisors of 18 are 1, 2,3,6,9 and 18. Where 1, 2,3,6 are the common divisors of 12 and 1 8, and 6 is their greatest common divisor.

The common divisor is only 1, which is called prime number. There are the following situations:

1 is coprime with any natural number.

Two adjacent natural numbers are coprime.

Two different prime numbers are coprime.

When the composite number is not a multiple of the prime number, the composite number and the prime number are coprime.

When the common divisor of two composite numbers is only 1, these two composite numbers are coprime. If any two numbers are coprime, they are said to be coprime.

If the smaller number is the divisor of the larger number, then the smaller number is the greatest common divisor of these two numbers.

If two numbers are prime numbers, their greatest common divisor is 1.

The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers. For example, the multiple of 2 is 2,4,6,8, 10, 12, 14, 16, 18.

The multiples of 3 are 3, 6, 9, 12, 15 and 18, where 6, 12 and 18 are common multiples of 2 and 3, and 6 is their least common multiple. .

If the larger number is a multiple of the smaller number, the larger number is the least common multiple of the two numbers.

If two numbers are prime numbers, then the product of these two numbers is their least common multiple.

The common divisor of several numbers is finite, while the common multiple of several numbers is infinite.

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