# GCF of 26 and 39

Created by: Team Maths - Examples.com, Last Updated: May 29, 2024

## GCF of 26 and 39

To find the Greatest Common Factor (GCF) of 26 and 39, you can use several methods. By listing the factors of each numbers, we find that the factors of 26 are 1, 2, 13, and 26, while the factors of 39 are 1, 3, 13, and 39. The common factors are 1 and 13, with the greatest common factor being 13. Using the prime factorization method, 26 can be expressed as 2 × 13 and 39 as 3 × 13, confirming that 13 is the common prime factor. Lastly, using the long division method, dividing 39 by 26 gives a remainder of 13, and dividing 26 by 13 gives a remainder of 0, leading to the GCF of 13. Therefore, the GCF of 26 and 39 is 13.

## Methods to Find GCF of 26 and 39

1. Prime Factorization Method
2. Long Division Method
3. Listing Common Factors

## GCF of 26 and 39 by Prime Factorization Method.

To find the Greatest Common Factor (GCF) of 26 and 39 using the prime factorization method, follow these steps:

### Step 1: Find the prime factorization of each number

Prime factorization of 26:

26 = 2 × 13

Prime factorization of 39:

39 = 3 × 13

### Step 2: Identify the common prime factors

The common prime factor of 26 and 39 is 13.

### Step 3: Multiply the common prime factors

Since the only common prime factor is 13, the GCF is 13.

## GCF of 26 and 39 by Long Division Method.

To find the Greatest Common Factor (GCF) of 26 and 39 using the long division method, follow these steps:

### Step 1: Divide the larger number by the smaller number

39 ÷ 26 = 1 with a remainder of 13.

### Step 2: Replace the larger number with the smaller number, and the smaller number with the remainder

Now, we have 26 and 13.

### Step 3: Repeat the division

26 ÷ 13 = 2 with a remainder of 0.

### Step 4: When the remainder is 0, the divisors is the GCF

The last non-zero remainder is 13. So, the GCF of 26 and 39 is 13.

## GCF of 26 and 39 by Listing Common Factors.

To find the Greatest Common Factor (GCF) of 26 and 39 by listing common factors, follow these steps:

Factors of 26:

1, 2, 13, 26

Factors of 39:

1, 3, 13, 39

### Step 2: Identify the common factors

Common factors of 26 and 39:

1, 13

### Step 3: Determine the greatest common factor

The largest common factor is 13. Therefore, the GCF of 26 and 39 is 13.

## How does the GCF help in dividing quantities evenly?

The GCF helps determine the largest group size that can evenly divide quantities.

## What is the product of 26 and 39?

The product of 26 and 39 is 1,014.

## Can the GCF be used to find the least common multiple (LCM)?

Yes, using the relationship: LCM(a, b) = (a × b) / GCF(a, b).

## Is the GCF of two numbers always smaller than the smallest number?

Yes, the GCF is always less than or equal to the smaller number.

## How do you verify the GCF of 26 and 39?

By dividing both numbers by the GCF to check if the quotients are integers.

## What is the smallest common factor of 26 and 39?

The smallest common factor is 1.

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