1 1
13 is a prime number)
Then 7007 is 7 2 * 1 1 * 13. The following are some basic rules of exponential notation: 2 2 * 2 3 = 2 5 (5 = 2+3) A X * A B = A (X 2 6/2 2 = 2 4 (4 = 6-2) (A X)/(A Y) = A (X. 6 ? 10 ? 15 = 1800 is the least common multiple of 12, 20, 30! ! ! In addition, some seemingly simple problems can also make these super-class students stumble, such as finding the least common multiple of 7 and 1 1 or 2, 3 and 5. Students often don't know what to do, because they can't say how to take the first step! We think all this is the result of their "learning to walk before learning", which greatly underestimates the subject of "least common multiple". You should know that there are three very basic mathematical concepts, namely "minimal", "common" and "multiple". Before mastering these concepts, it is a waste of time to learn the mechanized operation of short division. Moreover, they simply don't understand why this method will work. The so-called "learning" by rote often only brings a half-baked learning effect. After careful investigation of the method of finding the least common multiple by short division, it is not difficult to find that it contains the steps of finding the common factor. Then, why does the method of finding common multiple actually include the step of finding common factor? Why can't the method of finding the least common multiple of two numbers by short division be directly applied to finding the least common multiple of three numbers? In order to find the answers to these questions, it is necessary to introduce fundamental theorem of arithmetic, which is omitted here. However, if teachers do not face up to these potential learning difficulties, I am afraid it is difficult to expect students to learn this subject well. Since there are many problems in Professor Yu's method of finding the least common multiple by short division, why do parents, tutors and even some in-service teachers enjoy it? The reason is that they often unconsciously put "doing well in the exam" at a higher position than "understanding". The question that arises from this is why "answering the paper well" is not necessarily based on "understanding". The answer can be found in the following casual "ordinary" exam questions. "Find the least common multiple of 9 and 12. As long as students can accurately repeat the step of "finding the least common multiple by short division", teachers can naturally (and only) get full marks. However, it is impossible to test whether students understand the three very basic mathematical concepts of "minimal", "common" and "multiple". To put it bluntly, this question only requires students to "know a way to find the least common multiple of two numbers", but does not require students to "understand the meaning of the least common multiple". To exaggerate this practice, we can teach sixth graders to answer the following integer question: "Ask. Students don't necessarily need to know the meaning of integral, so they can get it according to the formula. Anyway, to understand the operating procedures, they only need to capture the laws of symbols, and don't even care about the meaning of indicators! Can students think that they have understood the meaning of integral just because they can write the indefinite integral correctly? How to break the above dilemma? Teachers might as well make more efforts to strengthen students' mastery of the concept of "common multiple" first! The most ideal way is to draw up more "alternative" topics, so that students can think more and avoid them blindly using short division to calculate. For example: Proposition 1: (a) Add the missing multiple to the appropriate position with the symbol "V". Multiples of 4: multiples of 4, 8, 16, 20, 24, 36, 40… 6: 6, 12, 18, 24, 36, 48 … (b) Write three different common multiples of 4 and 6. (c) Find the least common multiple of 4 and 6. (If students can't list the multiples of 4 correctly and clearly, then 12, 28 and 32 are missing; If the multiples of 6 miss 30 and 42, they will only mistake 24 for the least common multiple. Question 2: The minimum ten common multiples of a number are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 (a) and the minimum common multiples of 15. (b) The least common multiple of these two numbers and another number is 84. What is the other number? This question tests students' understanding of common multiples, and short division can't help. In (b), students can be encouraged to find the answer with the smallest value. Question 3: Circle the common multiples of the following groups. (a)9, 3: 24, 36, 45, 60, 108 (b)6, 8: 6, 16, 36, 72, 120 (if students can find the least common multiple of each group by short division, they may not know. So such questions help them find that other common multiples are only multiples of the least common multiple. Question 4: (a) Try to list all the factors of 12 and 14 respectively. (b) Two numbers have two common multiples of 12 and 14, and find the least common multiple of these two numbers. 3. () Parentheses are the greatest common factor. The brackets in [] are the least common multiple. 〔 3 × 3 × 3 × 5 × 5 × 7
2× 2× 3× 3× 3× 3× 5× 7× 7] = 2× 2× 3× 3× 5× 7× 7 (because I can't type, I can write it in the form of power) * * * * * * * *
2× 3× 1 1) = 2 (only 2 is needed to find the minimum power.
So their greatest common denominator is 2) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
2× 2× 3] = 2 × 2 × 3 × 5 × 7 (the prime factor that once appeared was 2 × 2 × 3 × 5 × 7, so their minimum common multiple was 2× 2× 3× 5× 7) * * * * * * * * * * * * * * * * * * * * * *. The prime factor within 8+000 is: 2.3.5.7.113.17.19.23.29.3438+0.37388.00000000001 79.83.89.97 A * * has 25 prime numbers: except 1 and himself.
There are no other factors. Total: Except 1 and yourself.
There are other factors.
1. What index symbol? Exponential notation is to decompose an integer into prime factors, and then record the numbers by exponential notation. For example, 600 = 2 * 2 * 3 * 5 * 5 (* stands for multiplication sign), 600 is 2 3 * 3 * 5 2 (stands for power sum and the number after it), and 7007 = 7 * 7.
1 1
13 is a prime number)
Then 7007 is 7 2 * 1 1 * 13. The following are some basic rules of exponential notation: 2 2 * 2 3 = 2 5 (5 = 2+3) A X * A B = A (X 2 6/2 2 = 2 4 (4 = 6-2) (A X)/(A Y) = A (X. What is factorization to find the least common multiple? A prime number ~ an integer greater than 1 has only 1 and itself, and there are no other factors. This integer is called a prime number. The smallest prime number is 2. 0 and 1 are neither prime numbers nor composite numbers. Which numbers in 1 ~ 100 are prime numbers? 235711192329 313741434753591677173798388. What is the sum of the composite numbers of 1 10 ~ 20? When10+12+14+15+16+18+20 =105 is added, one of the numbers is not added, and it is obtained. Solution 30+32+33+34+35+36+38+39+40-281= 36 What is the product of the two prime numbers closest to 45? Solution 43× 47 = 202 1 Example 4 What is the product of two prime numbers not greater than 60 and closest to 60? Solution 53× 59 = 3 127 II. What is a factor? What is a multiple? In multiplication, several multiplied numbers are called factors of product. For example: 2× 3× 5 = 30, then 2, 3 and 5 are all factors of 30, and 30 is the common multiple of these numbers; It can also be said that a number can be divisible by b number, and b number is a factor of a number. Conversely, a number is a multiple of b number. Common factor is that several factors with different numbers have the same factor, which is called common factor. For example: 18 and 24, the factors of these two numbers are: (the red number is the common factor of two numbers) 2006-12-18:14: 47 Supplement: 3. How to judge the application of common factor and common multiple? Usually, we can also judge whether we are looking for the greatest common factor or the smallest common multiple from the words of some problems in application problems, but there will be exceptions: the greatest common factor and the smallest common multiple ask: maximum, maximum, longest ... Question: minimum, minimum, at least ... Fourth, the solution of the greatest common factor: generally, we can find the greatest common factor in the following four ways (/kloc-0 So the common factor of 18 and 24 is: 1, 2,3,6, where 6 is the greatest common factor. (2) The prime factorization method is suitable for simple numbers. 18 = 2× 3× 324 = 2× 2× 3 Maximum common factor (both numbers exist): 2× 3 = 6 2006-12-1818:15. Example: How to find the greatest common factor of 1380 and 1794 by division? The key point to solve division: divide large numbers by decimals. 2006-1 2-1818:16:19 supplement:1. Draw three straight lines to separate the numbers 1380 and 1794. 2. Divide the larger number 1794 by the smaller number 1380. 3. The found multiple of 1 is placed at the far right of the straight line. 4. 1794- 1380=4 14。 5. Take 1380÷4 14 three times and put it on the far left. 6. 1380- 1242= 138。 7.4 14 ÷ 138 = 3 times (placed on the far right) ... 0.8. The last remaining 138 is the greatest common factor.
Reference:. qid=70060809049 15
1. Exponential notation is to decompose an integer by a prime factor, and then record the numbers by exponential notation, for example, 600=2*2*2*3*5*5 (* stands for the multiplication sign) 600 is 2 3 * 3 * 5 2 (stands for the number after the power sum) 2.
18 12 multiple: 12
24
36
48
60
72 .../kloc-multiple of 0/8: 18
36
54
Seventy two
90 ... which multiples are the same: 36
72...3. The common factor is the common factor of some numbers; That is, for example: 12.
18 12 factor: 1.
2
three
four
six
12 18 factor: 1.
2
three
six
nine
18 which factors are the same: 1.
2
three
six
Exponential notation is to decompose an integer into prime factors, and then record the numbers by exponential notation. For example, 600 = 2 * 2 * 3 * 5 * 5 (* stands for multiplication sign), 600 is 2 3 * 3 * 5 2 (stands for power sum and the number after it), and 7007 = 7 * 7.
1 1
13 is a prime number)
Then 7007 is 7 2 * 1 1 * 13. The following are some basic rules of exponential notation: 2 2 * 2 3 = 2 5 (5 = 2+3) A X * A B = A (X 2 6/2 2 = 2 4 (4 = 6-2) (A X)/(A Y) = A (X.
Find the H.C.F and L.C.H. (a)12 of the following two questions.
1812 = 22x318 = 2x32 so HCF = 2x3 = 6 LCM = 22x32 = 36 (b)16.
20
24 16 = 24 20 = 22 x 5 24 = 23 x 3 so HCF = 22 = 84 LCM = 24 x 3 x 5 = 240.
1. Exponential notation is to decompose an integer by a prime factor, and then record the number by exponential notation. For example, 600=2*2*2*3*5*5 (* stands for multiplication sign), and 600 is 2 3 * 3 * 5 2 (stands for power, what is the power of the following number).
1 1
13 is a prime number)
Then 7007 is 7 2 * 1 1 * 13. The following are some basic rules of exponential notation: 2 2 * 2 3 = 2 5 (5 = 2+3) a x * a b = a (x