How can you check that a prime factorization is correct?

Conditions

• The factors being multiplied must be the claimed prime factors.
• The product must equal the original number exactly.

Reasoning, step by step

1. List the prime factors obtained from the factor tree.
2. Multiply them together step by step.
3. Compare the final product with the original number.

Example

For the prime factorization of 48, which is $2 \times 2 \times 2 \times 2 \times 3$, you check it by calculating $2 \times 2 = 4$, $4 \times 2 = 8$, $8 \times 2 = 16$, and $16 \times 3 = 48$. Since the result is 48, the factorization is correct.

Common misconceptions

• Forgetting to multiply all the factors together.
• Assuming the factorization is correct just because the factors are prime, without checking if their product equals the original number.

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Explore next

• What is the prime factorization of 48?
• Do you have to start a factor tree with 2 for an even number?