What is the GCF of 60 and 100?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 60 and 100. To solve it, we need to identify the largest factor that both numbers share.

Answer

The GCF of 60 and 100 is 20.

Steps to Solve

Find the factors of each number
We start by listing the factors of 60 and 100. Factors are numbers that divide another number without leaving a remainder.
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Identify the common factors
Next, we find the factors that the two numbers share.
- Common factors of 60 and 100: 1, 2, 4, 5, 10, 20
Determine the greatest common factor
We now look for the greatest factor in the list of common factors.
The greatest common factor is 20.

The greatest common factor (GCF) of 60 and 100 is 20.

More Information

The greatest common factor is useful in simplifying fractions and finding common denominators. It represents the largest number that can evenly divide both original numbers. Knowing the GCF can also help when factoring polynomials or solving problems involving ratios.

Tips

Forgetting to list all factors: Ensure you list all factors correctly to find the common ones accurately.
Mistaking GCF for LCM: Remember, GCF looks for the largest shared factor, while LCM looks for the smallest common multiple.

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