Prime Factorization of 48

To find the prime factorization of 48, 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 48 is even, we start by dividing by 2. We can divide by 2 4 times:

After dividing by 2, we have 3 remaining.

We are left with 3, which is greater than 1.

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

Therefore, 3 is itself a prime number and is our final factor.

Now we combine all the prime factors we found:

Expanded form: 48 = 2 × 2 × 2 × 2 × 3

Exponential form: 48 = 2^4 × 3

We can verify: 2 × 2 × 2 × 2 × 3 = 48 ✓