What is the GCF of 63 and 72?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 63 and 72. To solve this, we will find all the factors of each number and then identify the largest factor that is common to both.
Answer
The greatest common factor of 63 and 72 is $9$.
Answer for screen readers
The greatest common factor of 63 and 72 is $9$.
Steps to Solve
- List the factors of 63 To find the factors of 63, we can divide it by all integers up to 63:
The factors of 63 are:
1, 3, 7, 9, 21, 63
- List the factors of 72 Next, we will do the same for 72, dividing it by all integers up to 72:
The factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Identify the common factors Now, we will find which factors appear in both lists:
Common factors of 63 and 72 are:
1, 3, 9
- Find the greatest common factor The greatest common factor is the largest number in the common factors list:
Hence, the GCF is:
$$ \text{GCF}(63, 72) = 9 $$
The greatest common factor of 63 and 72 is $9$.
More Information
The GCF is useful in simplifying fractions and finding common denominators. Factors are the building blocks of numbers, and understanding them helps with many areas in mathematics.
Tips
- Forgetting to list all factors completely.
- Overlooking common factors by missing smaller numbers.
- Confusing GCF with the least common multiple (LCM).
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