Prime Factorization of 108

To find the prime factorization of 108, we need to express it as a product of prime numbers.

We do this by repeatedly dividing by the smallest prime that divides evenly, starting with 2.

A prime number is only divisible by 1 and itself (2, 3, 5, 7, 11, 13, ...).

Since 108 is even, we start by dividing by 2. We can divide by 2 twice:

After dividing by 2, we have 27 remaining.

3 is a prime number that divides our current value. We can divide by 3 3 times:

After dividing by 3, we have 1 remaining.

Now we combine all the prime factors we found:

Expanded form: 108 = 2 × 2 × 3 × 3 × 3

Exponential form: 108 = 2^2 × 3^3

We can verify: 2 × 2 × 3 × 3 × 3 = 108 ✓