Factors, Multiples & Prime Numbers

Sep 23, 2026

Uploaded by Aran

Practice questions for learning factors, multiples, prime numbers, and related number theory skills. Students list factors and multiples, determine whether numbers are prime or composite, and compute prime factorizations. The worksheet also trains GCF and LCM calculations for given pairs, compares factor counts between numbers, and solves extended real-world problems involving equal groups and club meeting schedules using least common multiples and greatest common factors.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Questions

Factors, primes, and factorization

GCF and LCM

Real-world applications

Name: Factors, Multiples, & Prime Numbers Directions: Answer each question. Show work where needed. 1.) List all factors of 36: 2.) Is 97 a prime number? 3.) List the first 5 multiples of 14: 4.) What is the prime factorization of 60? 5.) Find the GCF of 48 and 64: 6.) What is the LCM of 6 and 15? 7.) Which of the following numbers are prime? 13, 21, 37, 49 → 8.) Which number is a common multiple of both 8 and 12? 24, 36, 48, 60 → 9.) Write the prime factorization of 72 using exponents: 10.) Circle all composite numbers: 17 18 19 21 23 11.) What is the GCF of 36 and 90? _______________ 12.) Find the LCM of 9 and 12: _______________ Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 1 13.) Is 111 a prime or composite number? 14.) Which number is a factor of both 45 and 60? 3, 7, 9, 11 → 15.) What is the smallest prime number? 16.) List all prime numbers between 30 and 50: 17.) Which has more factors: 28 or 36? 18.) What is the product of the first three prime numbers? 19.) Write a number that has exactly three distinct prime factors 20.) A school has 60 students in Band and 72 in Choir. What’s the greatest number of equal groups they can be split into with no student left out? 21.) Two school clubs are planning events: The Art Club meets every 12 days and the Science Club meets every 18 days Both clubs met today. a.) In how many days will both clubs meet on the same day again? b.) If there are 84 students in Art Club and 108 students in Science Club, and the school wants to divide each group into the largest equal teams possible, how many students will be in each team? c.) How many teams will there be in total? ______________ Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 2 ANSWER KEY 1.) 1, 2, 3, 4, 6, 9, 12, 18, 36 2.) Yes 3.) 14, 28, 42, 56, 70 4.) 2² × 3 × 5 5.) 16 6.) 30 7.) 13, 37 8.) 24 9.) 2³ × 3² 10.) 18, 21 11.) 18 12.) 36 13.) Composite 14.) 15 (but from list: 3 or 15; if 15 not listed, correct is 3) 15.) 2 16.) 31, 37, 41, 43, 47 17.) 36 18.) 2 × 3 × 5 = 30 19.) 30 (2 × 3 × 5), 42 (2 × 3 × 7), etc. 20.) GCF of 60 and 72 = 12 21.) a.) LCM of 12 and 18 = 36 days b.) GCF of 84 and 108 = 12 students per team c.) 84 ÷ 12 = 7 teams (Art) 108 ÷ 12 = 9 teams (Science) Total teams = 7 + 9 = 16 teams Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at ](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)[www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 3

FAQs

How do you find the factors of a number like 36?

List all positive integers that divide the number evenly. For 36, the answer key lists 1, 2, 3, 4, 6, 9, 12, 18, and 36.

What is the difference between prime and composite numbers?

Prime numbers have exactly two factors (1 and itself), while composite numbers have more than two factors. For example, 97 is prime, and 111 is composite.

How are GCF and LCM used in the worksheet’s problems?

GCF is used to find the greatest equal grouping size, while LCM is used for common meeting times or smallest common multiples. The answer key shows GCF of 60 and 72 is 12, and LCM of 12 and 18 is 36 days.

Sep 23, 2026

Uploaded by Aran

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