Every composite number can be expressed as a product of prime factors. We can use a factor tree to find the prime factors.

Example:

Find the prime factors of 36.

Solution:

The prime factors of 36 are 2 and 3.

We can write 36 as a product of prime factors: 2 × 2 × 3 × 3

The factor tree method is quite flexible – at each branch you can break the number into any factors until you reach the prime factors.

The result is the same: 36 = 3 × 2 × 2 × 3

Although the order of the factors may be different because we can start with different pairs of factors, every factor tree of 36 has the same prime factorization.

We can also use exponents to write the prime factorization.

36 = 2 ^{2} × 3 ^{2}

The following videos show more prime factorization examples using the factor tree.

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