GCD Master Quiz: Greatest Common Divisor Challenge

  • 6th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) Find the GCD of 36 and 48 using prime factorization.

Explanation

36 = 2×2×3×3; 48 = 2×2×2×2×3; Common factors = 2×2×3 = 12.

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About This Quiz
GCD Master Quiz: Greatest Common Divisor Challenge - Quiz

The GCD Master Challenge gives you a closer look at how numbers connect through their common factors. Each question guides you to compare values, break them down, and uncover the largest factor they share. You’ll see different situations where the greatest common divisor plays an important role, turning a simple... see moreidea into something surprisingly useful. Explore the problems at your own pace and enjoy strengthening your number sense along the way.
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2) Two friends have 45 and 60 apples. They want to divide them into equal baskets without leftovers. How many apples will each basket have?

Explanation

Factors of 45: 1, 3, 5, 9, 15, 45; Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; Common factors: 1, 3, 5, 15; GCD = 15.

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3) The GCD of 8 and 15 is 1 because they have no common prime factors.

Explanation

8 = 2×2×2; 15 = 3×5; No common primes, so GCD = 1.

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4) Find the GCD of 72 and 120 using the Euclidean Algorithm.

Explanation

120 ÷ 72 = 1 remainder 48; 72 ÷ 48 = 1 remainder 24; 48 ÷ 24 = 2 remainder 0; GCD = 24.

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5) Prime factorization of 100 = 2×2×5×5 and 140 = 2×2×5×7. What is their GCD?

Explanation

Common primes = 2×2×5 = 20. So GCD = 20.

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6) Which of these pairs have a GCD of 7?

Explanation

Each pair has multiples of 7. GCD = 7.

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7) A coach has 32 soccer balls and 40 cones. She wants identical sets with no leftovers. How many sets can she make?

Explanation

32 = 2×2×2×2×2; 40 = 2×2×2×5; Common primes = 2×2×2 = 8.

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8) Find the GCD of 54 and 81 using prime factorization.

Explanation

54 = 2×3×3×3; 81 = 3×3×3×3; Common = 3×3×3 = 27.

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9) Find GCD(60, 48) using division. 60 ÷ 48 = 1 remainder __; 48 ÷ __ = __ remainder 0

Explanation

60 ÷ 48 = 1 remainder 12; 48 ÷ 12 = 4 remainder 0; GCD = 12.

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10) A wall measures 84 cm by 126 cm. What is the largest square tile size that fits exactly?

Explanation

84 ÷ 21 = 4; 126 ÷ 21 = 6; So tile size = 21 cm.

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11) If one number divides the other, the GCD is the smaller number.

Explanation

Example: GCD(12, 48) = 12 because 48 is a multiple of 12.

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12) Find the GCD of 25 and 40.

Explanation

25 = 5×5; 40 = 2×2×2×5; Common factor = 5.

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13) Two buses arrive every 60 and 84 minutes. After how many minutes will both arrive together again?

Explanation

60 = 2×2×3×5; 84 = 2×2×3×7; GCD = 12; LCM = (60×84)/12 = 420.

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14) Find GCD(90, 135).

Explanation

90 = 2×3×3×5; 135 = 3×3×3×5; Common = 3×3×5 = 45.

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15) Which statements are true about the GCD?

Explanation

GCD divides both numbers, is smaller than both, and uses common factors.

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16) Find the GCD of 27 and 36.

Explanation

27 = 3×3×3; 36 = 2×2×3×3; Common = 3×3 = 9.

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17) Find GCD(64, 96) using the Euclidean Algorithm. 96 ÷ 64 = 1 remainder __; 64 ÷ __ = __ remainder 0

Explanation

96 ÷ 64 = 1 remainder 32; 64 ÷ 32 = 2 remainder 0; GCD = 32.

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18) The GCD of 36, 60, and 90 is 6.

Explanation

GCD(36, 60) = 12; GCD(12, 90) = 6; GCD = 6.

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19) Find GCD(84, 30) using the Euclidean Algorithm.

Explanation

84 ÷ 30 = 2 remainder 24; 30 ÷ 24 = 1 remainder 6; 24 ÷ 6 = 4 remainder 0; GCD = 6.

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20) A baker has 90 chocolate muffins and 150 vanilla muffins. He wants to pack them into boxes with equal numbers of each type. What is the greatest number of boxes he can make?

Explanation

GCD(90, 150) = 30. 30 boxes, each with 3 chocolate and 5 vanilla muffins.

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Find the GCD of 36 and 48 using prime factorization.
Two friends have 45 and 60 apples. They want to divide them into equal...
The GCD of 8 and 15 is 1 because they have no common prime factors.
Find the GCD of 72 and 120 using the Euclidean Algorithm.
Prime factorization of 100 = 2×2×5×5 and 140 = 2×2×5×7. What is...
Which of these pairs have a GCD of 7?
A coach has 32 soccer balls and 40 cones. She wants identical sets...
Find the GCD of 54 and 81 using prime factorization.
Find GCD(60, 48) using division. 60 ÷ 48 = 1 remainder __; 48 ÷ __ =...
A wall measures 84 cm by 126 cm. What is the largest square tile size...
If one number divides the other, the GCD is the smaller number.
Find the GCD of 25 and 40.
Two buses arrive every 60 and 84 minutes. After how many minutes will...
Find GCD(90, 135).
Which statements are true about the GCD?
Find the GCD of 27 and 36.
Find GCD(64, 96) using the Euclidean Algorithm. 96 ÷ 64 = 1 remainder...
The GCD of 36, 60, and 90 is 6.
Find GCD(84, 30) using the Euclidean Algorithm.
A baker has 90 chocolate muffins and 150 vanilla muffins. He wants to...
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