What is the GCF of 40 and 72?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the two numbers, 40 and 72. To determine the GCF, we need to find the factors of both numbers and identify the largest factor that they have in common.
Answer
The greatest common factor (GCF) of 40 and 72 is $8$.
Answer for screen readers
The greatest common factor (GCF) of 40 and 72 is $8$.
Steps to Solve
- Find the factors of 40
To find the GCF, we first need the factors of 40. The factors of 40 are the numbers that divide evenly into 40.
The factors of 40 are: $$ 1, 2, 4, 5, 8, 10, 20, 40 $$
- Find the factors of 72
Next, we do the same for 72. The factors of 72 are the numbers that divide evenly into 72.
The factors of 72 are: $$ 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 $$
- Identify the common factors
Now we look for the factors that both 40 and 72 share. The common factors are: $$ 1, 2, 4, 8 $$
- Determine the greatest common factor
Among the common factors, we need to find the greatest one. The greatest common factor (GCF) is: $$ 8 $$
The greatest common factor (GCF) of 40 and 72 is $8$.
More Information
The GCF is useful in simplifying fractions and finding common denominators. It's also fundamental in number theory and helps in understanding the relationships between numbers.
Tips
Common mistakes include:
- Forgetting to list all factors.
- Confusing common factors with prime factors. To avoid these, double-check your lists of factors and ensure you are identifying commonalities.
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