The product of three natural numbers is 180, and the sum of two natural numbers is equal to the third natural number I know the answer by enumeration What I want is the equation step 180 = 2 * 2 * 3 * 3 * 5 must be solved in this step? This is not enumeration

Let these three numbers be XYZ (x)

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1. (2013 · Zhangjiagang City simulation) it is known that Mn = C, CB = a, (a, B, C, D, m, n are all natural numbers), then the correct proportion in the following formula is () A. mn=baB. mn=abC. an=bmD. ma=bn
2. If three points a (- 2, - 2) B (0, m) C (n, 0) (Mn is not equal to 0) are collinear, What is 1 / M + 1 / N?
3. A = 2 × 3 × m, B = 3 × 5 × m (M is a natural number and m ≠ 0). If the greatest common divisor of a and B is 21, the least common multiple of a and B is 1______ ．
4. Any non-zero natural number can be judged by at least one factor () and the total number can be divided by 2
5. The product of three continuous natural numbers must be divisible by the combined number () The product of three continuous natural numbers must be divisible by the combined number () The scope of this problem is multiplication and division of integers and factorization
6. A natural number divisible by 2 must be a composite number I am a student of Fengtai No.1 Primary School. A three digit number composed of three natural numbers must be a multiple of three. √ or ×
7. With the smallest natural number, the smallest prime number and the smallest composite number, what are the three digit numbers that can be divided by 2, 3 and 5 at the same time? Write two
8. Use the smallest natural number, the smallest prime number and the smallest composite number to write the number divisible by 2, 3 and 5 at the same time
9. What is the smallest of the eight natural numbers with different divisors?
10. A natural number has 14 different divisors. What is the minimum number
11. 180 times m equals 183 times n. m and N are two adjacent natural numbers. What are m and N?
12. 180 * m = 183 * n. It is known that m and N are two adjacent natural numbers (M > n). What are m and N?
13. The quotient of natural number a divided by natural number B is 18. The least common multiple of a and B is 18______ ．
14. The quotient of natural number a divided by natural number B is 5. The least common multiple of these two natural numbers is () A. aB. bC. 5
15. Given that m and N are natural numbers and satisfy 168 + n square = m square, find m and n m. N is a natural number and satisfies 168 + M & # 178; = M & # 178;, find m and n
16. Satisfy m square - 3M
17. It is known that 8m ^ 2 + 1 is a perfect square number and M is a natural number Feedback: there is something wrong with your analysis. When k = 8, K (K + 1) / 2 = 36 is a perfect square number; when k = 288, K (K + 1) / 2 = (12 * 17) ^ 2 is also a perfect square number. Why do you say "when k > = 2, K and K + 1 are mutually prime, and can't be a perfect square number, so k = 1 or K = 0"?
18. How many values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number? Please don't paste it from Baidu. Their method is either not good or they can't understand it. It's better to draw inferences from one instance. If it's especially good, add it to 50 points, Here's how to eat beef noodles First, let m ^ 4-m ^ 2 + 4 = k ^ 2 Then m ^ 4-m ^ 2 = k ^ 2-4, so (m ^ 2-m) (m ^ 2 + m) = (K-2) (K + 2) ① If m ^ 2 and m are not zero and are integers, then we can get m ^ 2-m = K-2 or m ^ 2 + M = K + 2 (this is actually (a + b) (a-b) = (c + D) (C-D), where ABCD is a positive integer. If you give a value, you will find that a = C and B = D at any time ② If m ^ 2 or M = 0, then K does not care about it, because in any case K will have a value that meets the conditions of the problem, so directly solving m ^ 2-m = 0 or m ^ 2 + M = 0, we can get m = 0 or plus or minus 1, because m is a natural number, so m = 0,1,2
19. Square of P + square of M = square of N, where p prime number, m and N are natural numbers
20. If M and N are natural numbers and M is 8 times of N, then the greatest common factor of M and N is ()