Prime Factorization of 45

To find the prime factorization of 45, 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, ...).

45 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 5 remaining.

We are left with 5, which is greater than 1.

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

Therefore, 5 is itself a prime number and is our final factor.

Now we combine all the prime factors we found:

Expanded form: 45 = 3 × 3 × 5

Exponential form: 45 = 3^2 × 5

We can verify: 3 × 3 × 5 = 45 ✓