# GCF of 8 and 52

#### Understand the Problem

The question is asking for the greatest common factor (GCF) of the numbers 8 and 52. To find the GCF, we will identify the largest number that divides both 8 and 52 without leaving a remainder.

The greatest common factor of 8 and 52 is $4$.

The greatest common factor of 8 and 52 is $4$.

#### Steps to Solve

1. List the factors of each number

First, we need to find the factors of the numbers 8 and 52.

• The factors of 8 are: 1, 2, 4, 8
• The factors of 52 are: 1, 2, 4, 13, 26, 52
1. Identify the common factors

Next, we find the factors that are common to both numbers.

• Common factors of 8 and 52 are: 1, 2, 4
1. Find the greatest common factor

Finally, we identify the largest factor from the common factors found in the previous step.

The greatest common factor (GCF) is 4.

The greatest common factor of 8 and 52 is $4$.

The GCF helps in simplifying fractions, determining common denominators, and factoring polynomials. The GCF of two numbers is also useful in reducing or simplifying ratios when necessary. In this case, 4 is the largest number that divides both 8 and 52 without any remainder.

#### Tips

• Forgetting to list all factors of a number, which might result in missing common factors.
• Confusing GCF with the least common multiple (LCM).
• Rushing through the identification of common factors, leading to incorrect conclusions.
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