What are the set of numbers that when multiplied will make a certain number?

Answer 1

They are that number's factors.

If its the complete set of the smallest such numbers, they are the prime factors.

What's the difference? 4 and 15 are factors of 60: 4 x 15 = 60.

But the prime factors of 60 are 2 x 2 x 3 x 5. (Note that these are all prime numbers, which is where the term comes from.)

By multiplying the prime factors in different combinations -- such as 2 x (2 x 3) x 5 -- we can come up with all the possible combinations which lead to the original number.

Also note that the only prime factor of a Prime number is itself. Some teachers will tell you that the factors of a prime number are itself and 1, which is also true: 1 (known as unity) is special in that every number, when divided by it, remains the same. But 1 itself is not considered a prime number.