Prime Factorization of 81

To find the prime factorization of 81, 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, ...).

81 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 4 times:

After dividing by 3, we have 1 remaining.

Now we combine all the prime factors we found:

Expanded form: 81 = 3 × 3 × 3 × 3

Exponential form: 81 = 3^4

We can verify: 3 × 3 × 3 × 3 = 81 ✓