The process and meaning of number synthesis and decomposition are different. The composition of numbers, also known as the combination of numbers, means that a number (total) can be divided into several parts, and several parts can be combined into a number (total). For young children, the composition of numbers only refers to the combination of a number and two parts.

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Decomposition and synthesis formulas of numbers;

The decomposition of numbers refers to the decomposition of a positive integer into the products of several positive integers. For example, 4 can be decomposed into 2×2 or 1×4. The synthesis of numbers means that the product of several positive integers is equal to a positive integer. For example, 4 can be composed of 1, 2,4.

1 can be decomposed into any two multiplied numbers, such as1=/kloc-0 /×1= 2× (1/2) = 3× (1/3) and so on. For numbers greater than 1, there is a minimum prime factor, which can be used to decompose numbers quickly. For example, the smallest prime factor is 2, so any even number can be decomposed into a power of 2.

For odd numbers, except 1 and itself, the minimum prime factor is 3, so any odd number can be decomposed into the power of 3 plus 1. Any number greater than 1 can be expressed as the product of prime number plus 1, and the product of this prime number is the product of all prime numbers decomposed from this number.

Any positive integer can be expressed as the product of no more than four prime numbers plus 1. This theorem is called Legendre theorem. For a positive integer greater than 1, if there are only two prime factors in its prime factor decomposition formula, then it must be expressed as the power of 2 times the power of 3 plus 1. This theorem is called Ernie-Smith theorem.

For a positive integer greater than 1, if there are only two prime factors 2 and 3 in its prime factor decomposition formula, and the greatest common divisor of its power of 2 and power of 3 is 1, then it can definitely be expressed as the form of power of 2 multiplied by power of 3 plus 1. This theorem is called catalan theorem.

In a word, the decomposition and synthesis of numbers are very important basic knowledge in mathematics. By mastering the formulas and related theorems of decomposition and synthesis of numbers, we can better understand the essence and mathematical concepts of numbers and lay a solid foundation for future study.