List the factors of each number. Find the GCF of each pair of numbers: 15, 60.
The Correct Answer and Explanation is:
Correct Answer:
Factors of 15: 1, 3, 5, 15
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Greatest Common Factor (GCF): 15
Explanation:
To solve this problem, we begin by identifying all the factors of each number. A factor of a number is any whole number that divides it exactly, with no remainder.
Step 1: List the factors of 15.
To find the factors of 15, we test all whole numbers from 1 to 15 to see which divide evenly into 15.
- 15 ÷ 1 = 15
- 15 ÷ 3 = 5
- 15 ÷ 5 = 3
- 15 ÷ 15 = 1
So, the factors of 15 are: 1, 3, 5, 15
Step 2: List the factors of 60.
To find the factors of 60, we check all numbers from 1 to 60:
- 60 ÷ 1 = 60
- 60 ÷ 2 = 30
- 60 ÷ 3 = 20
- 60 ÷ 4 = 15
- 60 ÷ 5 = 12
- 60 ÷ 6 = 10
- 60 ÷ 10 = 6
- 60 ÷ 12 = 5
- 60 ÷ 15 = 4
- 60 ÷ 20 = 3
- 60 ÷ 30 = 2
- 60 ÷ 60 = 1
So, the factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Step 3: Find the common factors.
Now we compare the lists of factors for both numbers. The common factors are those that appear in both lists.
- Common factors of 15 and 60: 1, 3, 5, 15
Step 4: Identify the Greatest Common Factor.
The greatest of the common factors is 15, so the GCF of 15 and 60 is 15.
The GCF is useful in simplifying fractions, finding least common multiples, and solving real-life problems involving ratios.
