Practice Prime Factorization in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Writing a whole number as a product of prime numbers; every composite number has exactly one such representation (up to order).

Break a number into building blocks that cannot be split further (primes).

Example 1

easy
Find the prime factorization of 360 using a factor tree.

Example 2

hard
Use prime factorization to find \gcd(180, 252) and \text{lcm}(180, 252).

Example 3

easy
Write the prime factorization of 84 and use it to find all of its factors.

Example 4

medium
A rectangular garden can be arranged as a whole-number rectangle in exactly 6 different ways (including 1 \times n and n \times 1 as different). What is the smallest possible area for this garden?
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