Greatest Common Factor and Least Common Multiple: Grade 6 Math Test – PDF Download

Question 1: List factors (2 points)

List all the factors of each number.

1. 28 (1 point)
2. 45 (1 point)

Question 2: Prime factorizations (2 points)

Write the prime factorization of each number. Use exponents for repeated factors.

1. 84 (1 point)
2. 90 (1 point)

Question 3: Greatest common factors (2 points)

Find the greatest common factor of each pair.

1. 30 and 45 (1 point)
2. 64 and 96 (1 point)

Question 4: Least common multiples (2 points)

Find the least common multiple of each pair.

1. 8 and 10 (1 point)
2. 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.

1. \(40 + 24\) (1 point)
2. \(63 + 99\) (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.

1. Find the greatest number of bags she can fill. (1 point)
2. Find the number of granola bars and the number of juice boxes in each bag. (1 point)
3. 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.

1. Find the number of seconds until they next flash together. (2 points)
2. 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.