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
easyFind the prime factorization of .
Example 2
mediumSimplify using prime factorization.
Example 3
mediumWhat is the prime factorization of ?
Example 4
challengeWhat is the smallest positive integer to multiply by to make a perfect square?
Example 5
easyList the first five prime numbers.
Example 6
hardTrue or false: every integer greater than has a unique prime factorization. Name the theorem.
Example 7
mediumHow many positive divisors does have?
Example 8
challengeWhat is the smallest number with exactly divisors?
Example 9
easyFind the prime factorization of .
Example 10
mediumFind the prime factorization of .
Example 11
mediumFind the LCM of and using prime factorization.
Example 12
hardUse prime factorization to find and .
Example 13
mediumFind the prime factorization of .
Example 14
mediumFind all divisors of using its prime factorization.
Example 15
mediumUse prime factorization to find .
Example 16
mediumFind the prime factorization of .
Example 17
easyFind the prime factorization of .
Example 18
easyFind the prime factorization of using a factor tree.
Example 19
hardHow many positive divisors does have?
Example 20
hardFind the prime factorization of .