GCD Euclidean Algorithm Quiz: Find the GCD Easily

  • 6th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) If a divides b, then GCD(a, b) = a.

Explanation

If b = a×k, then GCD = a.

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About This Quiz
GCD Euclidean Algorithm Quiz: Find The GCD Easily - Quiz

This quiz takes you into the heart of the Euclidean Algorithm, a simple yet powerful way to find the greatest common divisor of two numbers. You’ll explore how repeated subtraction or division leads to the answer and why this method is still widely used today. Work through a mix of... see moreproblems, follow the steps, and build confidence in using this classic algorithm on your own.
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2) Find GCD(221, 119).

Explanation

221 ÷ 119 = 1 remainder 102; 119 ÷ 102 = 1 remainder 17; 102 ÷ 17 = 6 remainder 0. GCD = 17.

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3) Which steps correctly show the Euclidean Algorithm for GCD(156, 60)?

Explanation

Each step continues until remainder = 0. Last nonzero remainder 12 = GCD.

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4) Compute GCD(101, 37). 101 = 37×__ + __; 37 = 27×__ + __; 27 = 10×__ + __; 10 = 7×__ + __; 7 = 3×__ + __; 3 = 1×__ + 0

Explanation

101 ÷ 37 = 2 remainder 27; 37 ÷ 27 = 1 remainder 10; 27 ÷ 10 = 2 remainder 7; 10 ÷ 7 = 1 remainder 3; 7 ÷ 3 = 2 remainder 1; 3 ÷ 1 = 3 remainder 0. GCD = 1.

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5) Find GCD(144, 126).

Explanation

144 ÷ 126 = 1 remainder 18; 126 ÷ 18 = 7 remainder 0. GCD = 18.

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6) To find GCD of three numbers, compute GCD(a, b) first, then GCD(result, c).

Explanation

GCD(a, b, c) = GCD(GCD(a, b), c).

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7) Find GCD(36, 60, 90).

Explanation

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

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8) Select all correct ways to find GCD(128, 52).

Explanation

Following these steps gives last nonzero remainder 4 = GCD.

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9) Find GCD(255, 81). 255 = 81×__ + __; 81 = 12×__ + __; 12 = 9×__ + __; 9 = 3×__ + 0

Explanation

255 ÷ 81 = 3 remainder 12; 81 ÷ 12 = 6 remainder 9; 12 ÷ 9 = 1 remainder 3; 9 ÷ 3 = 3 remainder 0. GCD = 3.

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10) Find GCD(420, 156).

Explanation

420 ÷ 156 = 2 remainder 108; 156 ÷ 108 = 1 remainder 48; 108 ÷ 48 = 2 remainder 12; 48 ÷ 12 = 4 remainder 0. GCD = 12.

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11) If the remainder ever repeats in the Euclidean Algorithm, it continues forever.

Explanation

Remainders always decrease until reaching 0. The process ends with GCD.

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12) Find GCD(48, 18) using the Euclidean Algorithm.

Explanation

48 ÷ 18 = 2 remainder 12; 18 ÷ 12 = 1 remainder 6; 12 ÷ 6 = 2 remainder 0. GCD = 6.

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13) Find GCD(84, 30).

Explanation

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

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14) Complete the steps to find GCD(125, 20). 125 = 20m__ + __; 20 = 5m__ + 0

Explanation

To find GCD(125, 20), divide 125 by 20. You get 6 with a remainder of 5, so 125 = 20×6 + 5. Then divide 20 by 5, which gives 4 with a remainder of 0, so 20 = 5×4 + 0. Since 5 is the last nonzero remainder, the GCD is 5.

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15) If 96 = 36×2 + 24 and 36 = 24×1 + 12, then GCD(96, 36) = 12.

Explanation

Continuing: 24 ÷ 12 = 2 remainder 0. GCD = 12.

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16) Find GCD(99, 63).

Explanation

99 ÷ 63 = 1 remainder 36; 63 ÷ 36 = 1 remainder 27; 36 ÷ 27 = 1 remainder 9; 27 ÷ 9 = 3 remainder 0. GCD = 9.

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17) Select all true statements about the Euclidean Algorithm.

Explanation

Works for any positive integers. Divide larger by smaller. When remainder = 0, last nonzero remainder = GCD.

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18) Find GCD(140, 96).

Explanation

140 ÷ 96 = 1 remainder 44; 96 ÷ 44 = 2 remainder 8; 44 ÷ 8 = 5 remainder 4; 8 ÷ 4 = 2 remainder 0. GCD = 4.

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19) Find GCD(72, 50). 72 = 50×__ + __; 50 = 22×__ + __; 22 = 6×__ + __; 6 = 4×__ + __; 4 = 2×__ + 0

Explanation

72 ÷ 50 = 1 remainder 22; 50 ÷ 22 = 2 remainder 6; 22 ÷ 6 = 3 remainder 4; 6 ÷ 4 = 1 remainder 2; 4 ÷ 2 = 2 remainder 0. GCD = 2.

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20) Find GCD(270, 198).

Explanation

270 ÷ 198 = 1 remainder 72; 198 ÷ 72 = 2 remainder 54; 72 ÷ 54 = 1 remainder 18; 54 ÷ 18 = 3 remainder 0. GCD = 18.

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If a divides b, then GCD(a, b) = a.
Find GCD(221, 119).
Which steps correctly show the Euclidean Algorithm for GCD(156, 60)?
Compute GCD(101, 37). 101 = 37×__ + __; 37 = 27×__ + __; 27 = 10×__...
Find GCD(144, 126).
To find GCD of three numbers, compute GCD(a, b) first, then...
Find GCD(36, 60, 90).
Select all correct ways to find GCD(128, 52).
Find GCD(255, 81). 255 = 81×__ + __; 81 = 12×__ + __; 12 = 9×__ +...
Find GCD(420, 156).
If the remainder ever repeats in the Euclidean Algorithm, it continues...
Find GCD(48, 18) using the Euclidean Algorithm.
Find GCD(84, 30).
Complete the steps to find GCD(125, 20). 125 = 20m__ + __; 20 = 5m__ +...
If 96 = 36×2 + 24 and 36 = 24×1 + 12, then GCD(96, 36) = 12.
Find GCD(99, 63).
Select all true statements about the Euclidean Algorithm.
Find GCD(140, 96).
Find GCD(72, 50). 72 = 50×__ + __; 50 = 22×__ + __; 22 = 6×__ + __;...
Find GCD(270, 198).
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