Prime Factorization of 75

To find the prime factorization of 75, 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, ...).

75 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 once:

After dividing by 3, we have 25 remaining.

5 is a prime number that divides our current value. We can divide by 5 twice:

After dividing by 5, we have 1 remaining.

Now we combine all the prime factors we found:

Expanded form: 75 = 3 × 5 × 5

Exponential form: 75 = 3 × 5^2

We can verify: 3 × 5 × 5 = 75 ✓