How is finding the factors of a number different from finding the prime factorization of a number?

Finding factors of a number is different from finding the prime factorization.

Answer: Prime factorization of a number is expressing the number as a product of its prime factors. Further factorizing a number is to write the number as the product of its factors.

Let's see in detail.

Explanation:

Factors of a number are the numbers that divide the given number without leaving any remainder.

Prime factorization of a number is the process of writing all the prime factors of that number that can be multiplied to get back the given number.

For example:

Let's find the factors and prime factorization of 12.

Factors of 12 can be found in many ways:

12 = 1 × 12, which contains factors 1, and 12 (composite). 

or 12 = 2 × 6, which contains factors 2 (prime), and 6 (composite)

or 12 = 3 × 4, which contains factors 3 (prime), and 4 (composite)

The above three calculations are the factorization of the number 12.

or 12 = 2 × 2 × 3, which contains factors 2 (prime), and 3 (prime)

Here in this above calculation, we have performed the prime factorization of 12.

Hence, Factors of 12 = 1, 2, 3, 4, 6, 12, which contains 1, primes(2, 3) and composites(4, 6, 12)

Now,

Prime factorization of 12 = 2 × 2 × 3, which is unique.

Thus, finding the factors is different from the prime factorization.