What is the greatest common factor of 63 and 84?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 63 and 84. To solve this, we will determine the factors of both numbers and identify the largest one they have in common.
Answer
$21$
Answer for screen readers
The greatest common factor of 63 and 84 is $21$.
Steps to Solve
- Find the factors of 63
First, we need to find the factors of the number 63. The factors are the integers that can be multiplied together to get 63. The factors of 63 are:
1, 3, 7, 9, 21, 63.
- Find the factors of 84
Next, we will find the factors of the number 84. The factors of 84 are:
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
- Identify the common factors
Now we will list out the common factors between 63 and 84. Here they are:
1, 3, 7, 21.
- Determine the greatest common factor
Finally, we take the largest number from the common factors we found. The greatest common factor of 63 and 84 is: $$ 21 $$
The greatest common factor of 63 and 84 is $21$.
More Information
The greatest common factor (GCF) is an important concept in number theory and helps in simplifying fractions, finding common denominators, and solving problems involving ratios. The GCF of two numbers can be found using various methods, including listing the factors, as done here.
Tips
- Sometimes, people confuse the GCF with the least common multiple (LCM). Be sure to identify that we are looking for the largest factor common to both numbers, not the smallest multiple.
- Failing to list all factors accurately can lead to the wrong GCF. Always double-check your factors.