Prime Factorization of 117

To find the prime factorization of 117, 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, ...).

117 is an odd number, so it is not divisible by 2.

We move on to check the next prime number: 3.

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

After dividing by 3, we have 13 remaining.

We are left with 13, which is greater than 1.

13 cannot be divided by any prime smaller than its square root.

Therefore, 13 is itself a prime number and is our final factor.

Now we combine all the prime factors we found:

Expanded form: 117 = 3 × 3 × 13

Exponential form: 117 = 3^2 × 13

We can verify: 3 × 3 × 13 = 117 ✓