What is the prime factorization of 48?

Conditions

• The number being factored is 48.
• The terminal factors in the displayed tree are 2, 2, 2, 2, and 3.

Reasoning, step by step

1. Start with 48 and choose a factor pair, such as 4 and 12.
2. Break down 4 into 2 and 2.
3. Break down 12 into 3 and 4.
4. Break down the remaining 4 into 2 and 2.
5. Collect all the prime leaves: 2, 2, 2, 2, and 3.
6. Write the product: $48 = 2 \times 2 \times 2 \times 2 \times 3$.

Example

The video shows a factor tree for 48 starting with 4 and 12, which eventually branches into four 2s and one 3, resulting in the equation $48 = 2 \times 2 \times 2 \times 2 \times 3$.

Common misconceptions

• Listing each distinct prime only once, for example writing 48 as $2 \times 3$.
• Forgetting to include all repeated prime factors in the final product.

Watch the explanation

Explore next

• How can you check that a prime factorization is correct?
• Why are repeated prime factors written more than once?