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).

Showing a random 20 of 50 problems.

Example 1

easy
Find the prime factorization of 18.

Example 2

medium
Simplify 72 using prime factorization.

Example 3

medium
What is the prime factorization of 128?

Example 4

challenge
What is the smallest positive integer to multiply 90 by to make a perfect square?

Example 5

easy
List the first five prime numbers.

Example 6

hard
True or false: every integer greater than 1 has a unique prime factorization. Name the theorem.

Example 7

medium
How many positive divisors does 72 have?

Example 8

challenge
What is the smallest number with exactly 6 divisors?

Example 9

easy
Find the prime factorization of 45.

Example 10

medium
Find the prime factorization of 100.

Example 11

medium
Find the LCM of 8 and 12 using prime factorization.

Example 12

hard
Use prime factorization to find gcd⁡(120,200) and lcm(120,200).

Example 13

medium
Find the prime factorization of 144.

Example 14

medium
Find all divisors of 50 using its prime factorization.

Example 15

medium
Use prime factorization to find lcm(60,84).

Example 16

medium
Find the prime factorization of 210.

Example 17

easy
Find the prime factorization of 30.

Example 18

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

Example 19

hard
How many positive divisors does 360 have?

Example 20

hard
Find the prime factorization of 2310.