Practice Prime Numbers in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Integers greater than 1 whose only positive divisors are 1 and themselves—they cannot be factored further.
Primes can't be broken down further—they're the 'atoms' of multiplication.
Showing a random 20 of 50 problems.
Example 1
hardDetermine whether and explain.
Example 2
mediumWrite the prime factorization of .
Example 3
hardDetermine whether is prime.
Example 4
easyList all prime numbers between 20 and 40.
Example 5
mediumWhat is the smallest prime greater than ?
Example 6
hardWhat is the smallest positive integer with exactly distinct prime factors?
Example 7
mediumFind the prime factorization of .
Example 8
mediumFind the prime factorization of .
Example 9
mediumWhat is the largest prime factor of ?
Example 10
hardIf and are both prime and , prove that is divisible by .
Example 11
hardHow many divisors does have?
Example 12
easyList all primes between and .
Example 13
easyFind the prime factorization of .
Example 14
hardFind a prime such that , , and are all prime.
Example 15
easyIs a prime number?
Example 16
easyWhat is the only even prime number?
Example 17
challengeFind the smallest number with exactly three distinct prime factors.
Example 18
mediumIs prime?
Example 19
hardWhat is the sum of all primes less than ?
Example 20
challengeProve there is no largest prime (Euclid's idea, briefly).