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GCF of 26 and 52

GCF of 26 and 52 is the largest possible number that divides 26 and 52 exactly without any remainder. The factors of 26 and 52 are 1, 2, 13, 26 and 1, 2, 4, 13, 26, 52 respectively. There are 3 commonly used methods to find the GCF of 26 and 52 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 26 and 52
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 52?

Answer: GCF of 26 and 52 is 26.

Explanation:

The GCF of two non-zero integers, x(26) and y(52), is the greatest positive integer m(26) that divides both x(26) and y(52) without any remainder.

Methods to Find GCF of 26 and 52

The methods to find the GCF of 26 and 52 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 26 and 52 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 52 and Y = 26

GCF(52, 26) = GCF(26, 52 mod 26) = GCF(26, 0)
GCF(26, 0) = 26 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 26 and 52 is 26.

GCF of 26 and 52 by Listing Common Factors

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

There are 4 common factors of 26 and 52, that are 1, 2, 26, and 13. Therefore, the greatest common factor of 26 and 52 is 26.

GCF of 26 and 52 by Long Division

GCF of 26 and 52 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 52 (larger number) by 26 (smaller number).
Step 2: Since the remainder = 0, the divisor (26) is the GCF of 26 and 52.

The corresponding divisor (26) is the GCF of 26 and 52.

☛ Also Check:

GCF of 26 and 52 Examples

Example 1: The product of two numbers is 1352. If their GCF is 26, what is their LCM?

Solution:

Given: GCF = 26 and product of numbers = 1352
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1352/26
Therefore, the LCM is 52.
Example 2: Find the GCF of 26 and 52, if their LCM is 52.

Solution:

∵ LCM × GCF = 26 × 52
⇒ GCF(26, 52) = (26 × 52)/52 = 26
Therefore, the greatest common factor of 26 and 52 is 26.
Example 3: For two numbers, GCF = 26 and LCM = 52. If one number is 26, find the other number.

Solution:

Given: GCF (x, 26) = 26 and LCM (x, 26) = 52
∵ GCF × LCM = 26 × (x)
⇒ x = (GCF × LCM)/26
⇒ x = (26 × 52)/26
⇒ x = 52
Therefore, the other number is 52.

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FAQs on GCF of 26 and 52

What is the GCF of 26 and 52?

The GCF of 26 and 52 is 26. To calculate the GCF (Greatest Common Factor) of 26 and 52, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 52 = 1, 2, 4, 13, 26, 52) and choose the greatest factor that exactly divides both 26 and 52, i.e., 26.

How to Find the GCF of 26 and 52 by Prime Factorization?

To find the GCF of 26 and 52, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 52 = 2 × 2 × 13.
⇒ Since 2, 13 are common terms in the prime factorization of 26 and 52. Hence, GCF(26, 52) = 2 × 13 = 26
☛ Prime Number

How to Find the GCF of 26 and 52 by Long Division Method?

To find the GCF of 26, 52 using long division method, 52 is divided by 26. The corresponding divisor (26) when remainder equals 0 is taken as GCF.

If the GCF of 52 and 26 is 26, Find its LCM.

GCF(52, 26) × LCM(52, 26) = 52 × 26
Since the GCF of 52 and 26 = 26
⇒ 26 × LCM(52, 26) = 1352
Therefore, LCM = 52
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 26 and 52?

There are three commonly used methods to find the GCF of 26 and 52.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 26, 52?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 26 and 52, i.e. GCF × LCM = 26 × 52.

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