What is the GCF of 63 and 49?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 63 and 49. To solve this, we will determine the factors of each number and identify the largest factor that they have in common.
Answer
The greatest common factor of 63 and 49 is $7$.
Answer for screen readers
The greatest common factor of 63 and 49 is $7$.
Steps to Solve
- Find the factors of 63
List all the factors of 63. A factor is a number that divides evenly into another number. The factors of 63 are:
1, 3, 7, 9, 21, 63.
- Find the factors of 49
Similarly, list all the factors of 49. The factors of 49 are:
1, 7, 49.
- Identify the common factors
Next, find the factors that both 63 and 49 share. From the lists we created, the common factors are:
1, 7.
- Determine the greatest common factor
Finally, identify the largest common factor from the list. The greatest common factor (GCF) of 63 and 49 is:
The greatest common factor of 63 and 49 is $7$.
More Information
The greatest common factor (GCF), also known as the greatest common divisor (GCD), is an important concept in number theory. It is useful for simplifying fractions, as well as for solving problems involving divisibility.
Tips
- Forgetting to list all factors: Make sure to include every factor when determining GCF.
- Overlooking common factors: Check each factor carefully to ensure all common ones are identified.
- Only considering the largest number: The GCF is not always the largest number in the set; it must be common to both sets of factors.
