What does prime factorization mean in math? What does factorization mean?

Prime factorization means writing a number as the productof its prime factors.

Examples of prime factorizations.

What is the prime factorization of 8?

The number 8 is written as

8 = 2 * 4

2 is a prime number.

4 is not a prime number.

See Prime numbers 1 through 20.

We write the number 4 as

4 = 2 * 2

2 is a prime number.

Therefore, the prime factorization of 8 is

8 =

2 * 2 * 2

2 * 2 * 2

The prime factorization of 8 using exponents

8 = 2^{3}

What is the prime factorization of 24?

The number 24 can be factored as

24 = 3 * 8

Thus, we have factored 24. But all factors are not prime.

The number 8 is not a prime number.

The prime factorization of 8 is

8 =

2 * 2 * 2 =

2^{3}

2 * 2 * 2 =

2

Therefore, the prime factorization of 24 is

24 =

2 * 2 * 2 * 3

2 * 2 * 2 * 3

The prime factorization of 24 using exponents

24 = 2^{3} * 3