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GCF of 26 and 78

GCF of 26 and 78 is the largest possible number that divides 26 and 78 exactly without any remainder. The factors of 26 and 78 are 1, 2, 13, 26 and 1, 2, 3, 6, 13, 26, 39, 78 respectively. There are 3 commonly used methods to find the GCF of 26 and 78 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 26 and 78
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 78?

Answer: GCF of 26 and 78 is 26.

Explanation:

The GCF of two non-zero integers, x(26) and y(78), is the greatest positive integer m(26) that divides both x(26) and y(78) without any remainder.

Methods to Find GCF of 26 and 78

Let's look at the different methods for finding the GCF of 26 and 78.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 26 and 78 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78

There are 4 common factors of 26 and 78, that are 1, 2, 26, and 13. Therefore, the greatest common factor of 26 and 78 is 26.

GCF of 26 and 78 by Prime Factorization

Prime factorization of 26 and 78 is (2 × 13) and (2 × 3 × 13) respectively. As visible, 26 and 78 have common prime factors. Hence, the GCF of 26 and 78 is 2 × 13 = 26.

GCF of 26 and 78 by Long Division

GCF of 26 and 78 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 78 (larger number) by 26 (smaller number).
Step 2: Since the remainder = 0, the divisor (26) is the GCF of 26 and 78.

The corresponding divisor (26) is the GCF of 26 and 78.

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GCF of 26 and 78 Examples

Example 1: The product of two numbers is 2028. If their GCF is 26, what is their LCM?

Solution:

Given: GCF = 26 and product of numbers = 2028
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2028/26
Therefore, the LCM is 78.
Example 2: Find the greatest number that divides 26 and 78 exactly.

Solution:

The greatest number that divides 26 and 78 exactly is their greatest common factor, i.e. GCF of 26 and 78.
⇒ Factors of 26 and 78:
- Factors of 26 = 1, 2, 13, 26
- Factors of 78 = 1, 2, 3, 6, 13, 26, 39, 78
Therefore, the GCF of 26 and 78 is 26.
Example 3: For two numbers, GCF = 26 and LCM = 78. If one number is 78, find the other number.

Solution:

Given: GCF (z, 78) = 26 and LCM (z, 78) = 78
∵ GCF × LCM = 78 × (z)
⇒ z = (GCF × LCM)/78
⇒ z = (26 × 78)/78
⇒ z = 26
Therefore, the other number is 26.

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FAQs on GCF of 26 and 78

What is the GCF of 26 and 78?

The GCF of 26 and 78 is 26. To calculate the greatest common factor of 26 and 78, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 78 = 1, 2, 3, 6, 13, 26, 39, 78) and choose the greatest factor that exactly divides both 26 and 78, i.e., 26.

If the GCF of 78 and 26 is 26, Find its LCM.

GCF(78, 26) × LCM(78, 26) = 78 × 26
Since the GCF of 78 and 26 = 26
⇒ 26 × LCM(78, 26) = 2028
Therefore, LCM = 78
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What is the Relation Between LCM and GCF of 26, 78?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 26 and 78, i.e. GCF × LCM = 26 × 78.

How to Find the GCF of 26 and 78 by Prime Factorization?

To find the GCF of 26 and 78, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 78 = 2 × 3 × 13.
⇒ Since 2, 13 are common terms in the prime factorization of 26 and 78. Hence, GCF(26, 78) = 2 × 13 = 26
☛ What are Prime Numbers?

How to Find the GCF of 26 and 78 by Long Division Method?

To find the GCF of 26, 78 using long division method, 78 is divided by 26. The corresponding divisor (26) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 26 and 78?

There are three commonly used methods to find the GCF of 26 and 78.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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