Question

Find the prime factorization of 252.

Short answer

The prime factorization of 252 is$2^2\times 3^2\times 7$.

Step-by-step solution

Step 1. Prime factorization

The prime factorization of a number is calculated as follows.

• Find two factors whose product is the given number, and use these numbers to create two branches.
• If a factor is prime, that branch is complete. Circle the prime, like a bud on the tree.
• If a factor is not prime, write it as the product of two factors and continue the process.
• Write the composite number as the product of all the circled primes.

Step 2. Factor tree.

Use the prime factorization method defined in the previous step, the factor tree is drawn as shown below.

Step 3. Derivation.

From the factor tree, the prime factors of 252 are shown below.

$$\begin{gathered} 252=2\times 2\times 3\times 3\times 7 \\ 252=2^2\times 3^2\times 7 \end{gathered}$$

Step 4. Conclusion.

The prime factorization of 252 is$2^2\times 3^2\times 7$.