How can you express 48 as a product of its prime factors?

To express 48 as a product of its prime factors, we need to break it down into prime numbers that multiply together to give us 48.

First, we start by dividing 48 by the smallest prime number, which is 2:

• 48 ÷ 2 = 24
• 24 ÷ 2 = 12
• 12 ÷ 2 = 6
• 6 ÷ 2 = 3

Now we cannot divide 3 by 2 anymore because 3 is a prime number. Therefore, we stop here. Now, we gather all the prime factors we’ve found:

We divided by 2 four times and then reached 3, which is also a prime number. So, we can express 48 as:

48 = 2 × 2 × 2 × 2 × 3

For a cleaner representation, we can also write this using exponents:

48 = 24 × 3

Thus, the prime factorization of 48 is 2⁴ × 3.