Prime Factorization of 128

To find the prime factorization of 128, 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 128 is even, we start by dividing by 2. We can divide by 2 7 times:

After dividing by 2, we have 1 remaining.

Now we combine all the prime factors we found:

Expanded form: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Exponential form: 128 = 2^7

We can verify: 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 ✓