Practice using prime factorization, greatest common divisors, least common multiples, and modular arithmetic to solve number theory problems.
Read each problem carefully. Show your work in the space provided.
Finding common factors, common multiples, and remainders
Math - Grade 6-8
- 1
Find the greatest common divisor (GCD) of 24 and 36. Show one method you used.
- 2
Find the least common multiple (LCM) of 6 and 15.
- 3
Use prime factorization to find the GCD and LCM of 18 and 48.
- 4
A teacher has 32 pencils and 40 erasers. She wants to make identical supply bags with no pencils or erasers left over. What is the greatest number of supply bags she can make, and how many pencils and erasers will be in each bag?
- 5
Two blinking lights flash at the same time. One flashes every 8 seconds, and the other flashes every 12 seconds. In how many seconds will they flash together again?
- 6
Find the remainder when 47 is divided by 5. Write your answer using modular notation in the form 47 ≡ r mod 5.
- 7
Find the value of 38 mod 7.
- 8
A clock shows 9:00. What time will it show 17 hours later? Explain using modular arithmetic.
- 9
Complete the statement: 29 ≡ ___ mod 6. Explain your answer.
- 10
Which numbers from this list are congruent to 2 mod 5: 7, 10, 12, 17, 21, 27? Explain how you know.
- 11
Find the GCD and LCM of 45 and 60.
- 12
A number leaves a remainder of 1 when divided by 4. Which of these could be the number: 18, 21, 25, 30, 33? List all possible answers and explain.