Prime Factorization of 126

To find the prime factorization of 126, 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 126 is even, we start by dividing by 2. We can divide by 2 once:

After dividing by 2, we have 63 remaining.

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

After dividing by 3, we have 7 remaining.

We are left with 7, which is greater than 1.

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

Therefore, 7 is itself a prime number and is our final factor.

Now we combine all the prime factors we found:

Expanded form: 126 = 2 × 3 × 3 × 7

Exponential form: 126 = 2 × 3^2 × 7

We can verify: 2 × 3 × 3 × 7 = 126 ✓