The factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104.

From these lists, we can see that the factors that 52 and 104 have in common are 1, 2, 4, 13, 26, and 52. The greatest of these factors is 52. Therefore, the GCF of 52 and 104 is 52.

Another method to find the GCF is to use prime factorization. We can write 52 and 104 as the product of their prime factors:

52 = 2^2 * 13 104 = 2^3 * 13

The factors they have in common are the product of the common prime factors, which are 2 and 13. The highest power of 2 that divides both 52 and 104 is 2^2, and the highest power of 13 that divides both is 13^1. Therefore, the GCF of 52 and 104 is 2^2 * 13 = 52, which is the same result as before.

## What is GCF of 52 and 104

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The GCF (Greatest Common Factor) of 52 and 104 is 52.

One way to find the GCF is to list the factors of each number and find the greatest factor they have in common. The factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 104 are 1, 2, 4, 8, 13, 26, 52, and 104. The greatest factor that they have in common is 52.

Another way to find the GCF is to use prime factorization. We can write 52 and 104 as the product of their prime factors:

52 = 2 x 2 x 13 104 = 2 x 2 x 2 x 13

The common prime factors are 2 and 13. The highest power of 2 that divides both 52 and 104 is 2 x 2 = 4, and the highest power of 13 that divides both is 13 x 1 = 13. Therefore, the GCF of 52 and 104 is 4 x 13 = 52.

## Methods to Find GCF of 52 and 104

There are several methods to find the GCF (Greatest Common Factor) of 52 and 104:

**Method 1: Listing Factors**

- List the factors of each number.
- Find the factors that they have in common.
- Choose the greatest common factor.

Factors of 52: 1, 2, 4, 13, 26, 52 Factors of 104: 1, 2, 4, 8, 13, 26, 52, 104

The factors they have in common are 1, 2, 4, 13, 26, and 52. Therefore, the GCF of 52 and 104 is 52.

**Method 2: Prime Factorization**

- Write both numbers as a product of their prime factors.
- Find the common prime factors.
- Multiply the common prime factors with the smallest exponents.

Prime factorization of 52: 2 x 2 x 13 Prime factorization of 104: 2 x 2 x 2 x 13

The common prime factors are 2 and 13. The highest power of 2 that divides both 52 and 104 is 2 x 2 = 4. The highest power of 13 that divides both 52 and 104 is 13 x 1 = 13. Therefore, the GCF of 52 and 104 is 4 x 13 = 52.

**Method 3: Euclidean Algorithm**

- Divide the larger number by the smaller number and find the remainder.
- Divide the smaller number by the remainder and find the new remainder.
- Continue until the remainder is zero.
- The GCF is the last nonzero remainder.

104 ÷ 52 = 2 with a remainder of 0 52 ÷ 0 = 0 with a remainder of 52

The last nonzero remainder is 52. Therefore, the GCF of 52 and 104 is 52.