Prime Factorization of 66

To find the prime factorization of 66, 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 66 is even, we start by dividing by 2. We can divide by 2 once:

After dividing by 2, we have 33 remaining.

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

After dividing by 3, we have 11 remaining.

We are left with 11, which is greater than 1.

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

Therefore, 11 is itself a prime number and is our final factor.

Now we combine all the prime factors we found:

Expanded form: 66 = 2 × 3 × 11

Exponential form: 66 = 2 × 3 × 11

We can verify: 2 × 3 × 11 = 66 ✓