Question

Чем отличается разложение числа на множители и на простые множители?

Answer 1

Множители - это любые числа - произведение которых дано заданному

а простые множители - это простые числа (2; 3; 5; 7; ...)
в разложении на простые множители присутствуют ТОЛЬКО простые числа

Answer 2

Difference Between Factoring a Number and Factoring it into Prime Factors

When we talk about factoring a number, we are essentially breaking it down into its constituent parts. However, there is a distinction between factoring a number into its factors and factoring it into prime factors.

Factoring a Number: - Factoring a number involves breaking it down into its factors, which can be any integers that multiply together to give the original number. - For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Factoring a Number into Prime Factors: - Factoring a number into prime factors involves breaking it down into a product of prime numbers. - Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. - For example, the prime factorization of 12 is 2 * 2 * 3.

In summary, while factoring a number involves finding any combination of factors, factoring it into prime factors involves breaking it down into a product of prime numbers.

[[Source 2]]