What is prime factorization?

Conditions

• The starting number is a positive integer greater than 1.
• The final factors must all be prime numbers.
• The product of the final prime factors must equal the original number.

Reasoning, step by step

1. Identify the number to be factored.
2. Break the number down into its prime factors.
3. Verify that the product of these prime factors equals the original number.

Example

For the number 30, the prime factorization is $30 = 2 \times 3 \times 5$, because 2, 3, and 5 are prime numbers and their product is 30.

Common misconceptions

• Assuming that any factorization (like $30 = 5 \times 6$) is a prime factorization; 6 is not prime.
• Thinking that the order of the prime factors matters; $2 \times 3 \times 5$ is the same as $5 \times 3 \times 2$.

Watch the explanation

Explore next

• How do you use a factor tree to find prime factors?
• Why do you stop breaking down a factor once it is prime?