Prime Factorization of 56

To find the prime factorization of 56, 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 56 is even, we start by dividing by 2. We can divide by 2 3 times:

After dividing by 2, 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: 56 = 2 × 2 × 2 × 7

Exponential form: 56 = 2^3 × 7

We can verify: 2 × 2 × 2 × 7 = 56 ✓