This 45-minute test covers factors, primes, GCF, and LCM from Common Core 6.NS.B.4. It has 9 questions worth 20 points in total. Show your work for every question, and write each prime factorization with exponents where factors repeat.
- Grade: Grade 6
- Chapter: Greatest Common Factor and Least Common Multiple
- Common Core: 6.NS.B.4
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 2 pts)
Question 1: List factors (2 points)
List all the factors of each number.
- 28 (1 point)
- 45 (1 point)
Question 2: Prime factorizations (2 points)
Write the prime factorization of each number. Use exponents for repeated factors.
- 84 (1 point)
- 90 (1 point)
Question 3: Greatest common factors (2 points)
Find the greatest common factor of each pair.
- 30 and 45 (1 point)
- 64 and 96 (1 point)
Question 4: Least common multiples (2 points)
Find the least common multiple of each pair.
- 8 and 10 (1 point)
- 9 and 6 (1 point)
Question 5: Rewrite sums as products (2 points)
Use the greatest common factor and the distributive property to rewrite each sum as a product.
- \(40 + 24\) (1 point)
- \(63 + 99\) (1 point)
Question 6: Snack bags (3 points)
Aisha has 36 granola bars and 54 juice boxes. She puts them into identical snack bags with nothing left over.
- Find the greatest number of bags she can fill. (1 point)
- Find the number of granola bars and the number of juice boxes in each bag. (1 point)
- Write \(36 + 54\) as a product using the greatest common factor. (1 point)
Question 7: Flashing lights (3 points)
A lighthouse flashes every 9 seconds and a buoy light flashes every 12 seconds. They flash together at the start.
- Find the number of seconds until they next flash together. (2 points)
- Find the number of flashes the buoy makes from the start until then, counting the flash at the end but not the one at the start. (1 point)
Question 8: Find the error (2 points)
Noah says the greatest common factor of 18 and 27 is 54. Explain his mistake and find the correct greatest common factor.
Question 9: Prime or not (2 points)
Mei says that 51 is a prime number. Determine whether she is correct and justify the answer.
See every chapter on the Grade 6 math page.

