What is the prime factorization of 108?

The prime factorization of a number involves breaking it down into its basic building blocks, which are prime numbers. For the number 108, we can find its prime factors through division.

Step-by-Step Factorization

To factor 108, we start by dividing it by the smallest prime number, which is 2:

• 108 ÷ 2 = 54
• 54 ÷ 2 = 27

Now, 27 is not divisible by 2, so we move to the next prime number, which is 3:

• 27 ÷ 3 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Final Prime Factors

Now that we have reached 1, we can list the prime factors we used:

• 2 (used twice)
• 3 (used three times)

Thus, the prime factorization of 108 can be expressed as:

2² × 3³