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 1818.

Example 2

medium
Simplify 72\sqrt{72} using prime factorization.

Example 3

medium
What is the prime factorization of 128128?

Example 4

challenge
What is the smallest positive integer to multiply 9090 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 11 has a unique prime factorization. Name the theorem.

Example 7

medium
How many positive divisors does 7272 have?

Example 8

challenge
What is the smallest number with exactly 66 divisors?

Example 9

easy
Find the prime factorization of 4545.

Example 10

medium
Find the prime factorization of 100100.

Example 11

medium
Find the LCM of 88 and 1212 using prime factorization.

Example 12

hard
Use prime factorization to find gcdโก(120,200)\gcd(120, 200) and lcm(120,200)\text{lcm}(120, 200).

Example 13

medium
Find the prime factorization of 144144.

Example 14

medium
Find all divisors of 5050 using its prime factorization.

Example 15

medium
Use prime factorization to find lcm(60,84)\text{lcm}(60, 84).

Example 16

medium
Find the prime factorization of 210210.

Example 17

easy
Find the prime factorization of 3030.

Example 18

easy
Find the prime factorization of 360360 using a factor tree.

Example 19

hard
How many positive divisors does 360360 have?

Example 20

hard
Find the prime factorization of 23102310.