Prime factorization of a number means to write the number as a product of prime numbers.

What is the prime factorization of 10?

The number 10 is written as

10 = 2 * 5

Both 2 and 5 are prime numbers.

See Prime numbers 1 through 20.

Therefore, the prime factorization of 10 is

10 = 2 * 5

What is the prime factorization of 48?

The number 48 can be factored as

48 = 2 * 24

Thus, we have factored 48. But all the factors are not prime.

2 is a prime number and 24 is not.

The prime factorization of 24 is

24 =

2 * 2 * 2 * 3 =

2^{3} * 3

2 * 2 * 2 * 3 =

2

Therefore, the prime factorization of 48 is

48 =

2 * 2 * 2 * 2 * 3

2 * 2 * 2 * 2 * 3

The prime factorization of 48 using exponents

48 = 2^{4} * 3