Determine the greatest common factor. 15 and 20
The Correct Answer and Explanation is:
The correct answer is 5.
Explanation:
To find the greatest common factor (GCF) of 15 and 20, follow these steps:
Step 1: Find the factors of each number
- Factors of 15 are: 1, 3, 5, 15
- Factors of 20 are: 1, 2, 4, 5, 10, 20
Step 2: Identify the common factors
The common factors of 15 and 20 are: 1 and 5
Step 3: Find the greatest common factor
The largest number in the list of common factors is 5, so the GCF of 15 and 20 is 5.
Why is finding the GCF important?
The GCF is useful when simplifying fractions, dividing numbers evenly, or solving problems involving ratios and proportions. It represents the largest number that can exactly divide both numbers without leaving a remainder.
For example, if you have 15 apples and 20 oranges, and you want to pack them into identical groups with no leftovers, the largest number of groups you can make is 5, because 5 is the greatest number that evenly divides both 15 and 20.
Prime Factorization Method (alternative approach)
Another method to find the GCF is by using prime factorization:
- Prime factors of 15 are: 3 × 5
- Prime factors of 20 are: 2 × 2 × 5
The common prime factor is 5, so the GCF is 5.
This method is reliable and especially useful for larger numbers. It helps break down numbers into their basic building blocks and shows clearly which factors they share.
In conclusion, whether using the list of factors or prime factorization, the greatest common factor of 15 and 20 is 5, which means 5 is the largest number that can divide both numbers exactly.
