Examples of Greatest Common Divisor (GCD) Examples

Discover practical examples of the Greatest Common Divisor (GCD) with clear explanations and contexts.
By Taylor

Understanding the Greatest Common Divisor (GCD)

The Greatest Common Divisor, or GCD, is the largest positive integer that divides two or more numbers without leaving a remainder. Understanding the GCD can be useful in various everyday situations, from simplifying fractions to solving problems in number theory. Let’s explore three diverse and practical examples that illustrate the concept of GCD in action.

Example 1: Sharing Candies with Friends

Imagine you have 12 candies, and your friend has 18 candies. You both want to share your candies equally among your friends, but you want to ensure that everyone gets the same number of candies without breaking any. To find out how many friends can share the candies equally, you need to determine the GCD of 12 and 18.

To calculate this:

  1. List the factors of both numbers.
  • Factors of 12: 1, 2, 3, 4, 6, 12

  • Factors of 18: 1, 2, 3, 6, 9, 18

    1. Identify the largest common factor.

  • The common factors are: 1, 2, 3, and 6.

  • The GCD is 6.

This means you can share the candies with 6 friends, and each friend will receive 2 candies (12/6) or 3 candies (18/6), depending on how you want to distribute them.

Notes

You can experiment with other numbers of candies, like 15 and 25, to see how the GCD helps in distributing items evenly.

Example 2: Dividing Land into Equal Plots

Suppose you own a piece of land that measures 40 meters by 60 meters, and you want to divide it into smaller plots that are all the same size for a community garden. To find the maximum size of each plot that can fit into the land without any leftover space, you need to compute the GCD of the two dimensions, 40 and 60.

Here’s how:

  1. Find the factors of both numbers.
  • Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

  • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

    1. From the list, identify the largest common factor.

  • The common factors are: 1, 2, 4, 5, 10, 20.

  • The GCD is 20.

This means you can create plots measuring 20 meters by 20 meters without any leftover land, as both dimensions of your land can be evenly divided by 20.

Notes

You can try different dimensions, like 30 meters by 45 meters, to see how the GCD can help you maximize the size of your plots.

Example 3: Organizing a Sports Tournament

Imagine you are organizing a sports tournament where two teams are competing. Team A has 24 players, and Team B has 36 players. To create fair game matches, you want to form teams with equal numbers of players. To find the largest size for each team, you need to calculate the GCD of 24 and 36.

Here’s how:

  1. Identify the factors of both numbers.
  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

  • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

    1. Find the largest common factor.

  • The common factors are: 1, 2, 3, 4, 6, 12.

  • The GCD is 12.

You can form teams of 12 players each, ensuring that both teams have an equal number of players in each match.

Notes

You can also explore other scenarios, like 18 players versus 30 players, to see how the GCD can help in organizing teams effectively.