What is the greatest common factor of 30 and 5?

Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 30 and 5. To solve this, we will find the factors of both numbers and identify the largest one they share.

Answer

The greatest common factor of 30 and 5 is $5$.

Steps to Solve

List the factors of each number
First, let's find the factors of both 30 and 5.

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 5 are: 1, 5

Identify the common factors
Next, we need to determine which factors are common to both lists.

The common factors of 30 and 5 are: 1, 5

Find the greatest common factor
Finally, we select the largest common factor from the list above.

The greatest common factor (GCF) of 30 and 5 is 5.

The greatest common factor of 30 and 5 is 5.

More Information

The greatest common factor (GCF) is helpful in simplifying fractions or finding the least common multiple (LCM). In this case, since 5 is a factor of 30, it's the largest number that divides both evenly.

Tips

Ignoring the smallest number: Sometimes students forget to check the factors of the smaller number, leading to missing common factors. Always list factors for both numbers.
Mistaking GCF for LCM: Some may confuse GCF with least common multiple (LCM). Remember, GCF is the largest shared factor, while LCM is the smallest shared multiple.

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