Applying GCD in Real-World Contexts

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| Questions: 10 | Updated: Nov 7, 2025
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1) Two marching bands have 48 and 60 students. They want to line up in rows with the same number of students in each row and no one left out. What is the greatest number of students per row?

Explanation

Factors of 48: {1,2,3,4,6,8,12,16,24,48}. Factors of 60: {1,2,3,4,5,6,10,12,15,20,30,60}. GCD=12.

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About This Quiz
Applying GCD In Real-world Contexts - Quiz

Numbers aren’t just for the classroom—they solve real problems too! In this quiz, you’ll use GCD to split groups evenly, arrange objects without leftovers, and design fair divisions in everyday scenarios. We bring you this quiz to show how the greatest common divisor makes problem-solving practical and powerful.

2) A park has 42 benches and 56 trash bins. The city wants to group them into identical sections with no leftovers. What is the largest number of sections?

Explanation

Factors of 42: {1,2,3,6,7,14,21,42}. Factors of 56: {1,2,4,7,8,14,28,56}. GCD=14.

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3) A farmer has 30 sheep and 45 goats. He wants to arrange them into equal pens, mixing sheep and goats, with no animals left out. What is the greatest number of pens?

Explanation

Factors of 30: {1,2,3,5,6,10,15,30}. Factors of 45: {1,3,5,9,15,45}. GCD=15.

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4) Two playground slides are 48 feet and 64 feet long. The manager wants to build equal-length safety mats for both slides. What is the longest mat length that works for both?

Explanation

GCD of 48 and 64 = 16.

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5) A gardener plants 72 roses and 108 tulips in equal rows. What is the maximum number of rows she can make with no leftovers?

Explanation

GCD of 72 and 108 = 18.

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6) A coach has 32 soccer balls and 40 cones. She wants to divide them into identical training kits. What is the greatest number of kits she can make?

Explanation

GCD of 32 and 40 = 8.

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7) Two buses arrive at a station every 60 minutes and 84 minutes. After how many minutes will both buses be at the station together?

Explanation

LCM(60,84)=420 minutes.

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8) A mural wall is 72 cm by 108 cm. The artist wants to tile it with the largest square tiles possible, with no cutting. What is the side length of each square tile?

Explanation

GCD of 72 and 108 = 36 cm.

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9) A music teacher has 45 violins and 60 flutes. She wants to form identical orchestra groups. What is the maximum number of groups?

Explanation

GCD of 45 and 60 = 15.

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10) A video game tournament has 84 players and 126 players in two divisions. The organizer wants to split them into groups of the same size, with no players left out. What is the largest group size?

Explanation

The largest group size is determined by finding the greatest common divisor of 84 and 126, which is 42.

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Two marching bands have 48 and 60 students. They want to line up in...
A park has 42 benches and 56 trash bins. The city wants to group them...
A farmer has 30 sheep and 45 goats. He wants to arrange them into...
Two playground slides are 48 feet and 64 feet long. The manager wants...
A gardener plants 72 roses and 108 tulips in equal rows. What is the...
A coach has 32 soccer balls and 40 cones. She wants to divide them...
Two buses arrive at a station every 60 minutes and 84 minutes. After...
A mural wall is 72 cm by 108 cm. The artist wants to tile it with the...
A music teacher has 45 violins and 60 flutes. She wants to form...
A video game tournament has 84 players and 126 players in two...
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