GCD of 72 and 5
Understand the Problem
The question is asking for the greatest common divisor (GCD) of the numbers 72 and 5. To solve this, we will identify the largest integer that divides both numbers without leaving a remainder.
Answer
The greatest common divisor of 72 and 5 is $1$.
Answer for screen readers
The greatest common divisor of 72 and 5 is $1$.
Steps to Solve
- Identify the numbers
We are given two numbers: 72 and 5.
- List the factors
Next, we need to find the factors of each number.
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
- The factors of 5 are: 1, 5.
- Find the common factors
Now, we compare the factors of both numbers to find the common factors:
- The only common factor between 72 and 5 is: 1.
- Determine the greatest common divisor (GCD)
The greatest common divisor is the highest number that appears in the list of common factors. In this case, the GCD of 72 and 5 is:
$$ \text{GCD}(72, 5) = 1 $$
The greatest common divisor of 72 and 5 is $1$.
More Information
The GCD is useful in many applications, including simplifying fractions and solving problems involving ratios. It helps in determining how many equal parts can be made from two different sets of items.
Tips
- One common mistake is assuming that the GCD must be greater than 1. In this case, since 72 and 5 share no other factors besides 1, it's easy to overlook that.
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