What is the GCF of 49 and 14?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 49 and 14. To solve it, we will find the factors of both numbers and determine the largest factor they have in common.
Answer
The GCF of 49 and 14 is $7$.
Answer for screen readers
The greatest common factor of 49 and 14 is $7$.
Steps to Solve
- List the factors of each number
We will first find the factors of 49. The factors of 49 are: 1, 7, 49
Now, let's find the factors of 14. The factors of 14 are: 1, 2, 7, 14
- Identify the common factors
Next, we will identify the factors that 49 and 14 have in common. From the lists:
- Factors of 49: 1, 7, 49
- Factors of 14: 1, 2, 7, 14
The common factors are 1 and 7.
- Determine the greatest common factor
Finally, we need to find the greatest of the common factors. The largest common factor between 1 and 7 is:
$$ \text{GCF} = 7 $$
The greatest common factor of 49 and 14 is $7$.
More Information
The greatest common factor (GCF) is a way of finding the largest number that can evenly divide two or more numbers without leaving a remainder. In this case, both 49 and 14 can be divided by 7.
Tips
- Forgetting to list all factors: Ensure that all factors of each number are identified.
- Misidentifying common factors: Double-check to ensure that only the factors that appear in both lists are considered.
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