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GCF of 26 and 36

GCF of 26 and 36 is the largest possible number that divides 26 and 36 exactly without any remainder. The factors of 26 and 36 are 1, 2, 13, 26 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 26 and 36 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 26 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 36?

Answer: GCF of 26 and 36 is 2.

Explanation:

The GCF of two non-zero integers, x(26) and y(36), is the greatest positive integer m(2) that divides both x(26) and y(36) without any remainder.

Methods to Find GCF of 26 and 36

The methods to find the GCF of 26 and 36 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 26 and 36 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 = 36 and Y = 26

GCF(36, 26) = GCF(26, 36 mod 26) = GCF(26, 10)
GCF(26, 10) = GCF(10, 26 mod 10) = GCF(10, 6)
GCF(10, 6) = GCF(6, 10 mod 6) = GCF(6, 4)
GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 26 and 36 is 2.

GCF of 26 and 36 by Long Division

GCF of 26 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 26 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (26) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 26 and 36.

GCF of 26 and 36 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 2 common factors of 26 and 36, that are 1 and 2. Therefore, the greatest common factor of 26 and 36 is 2.

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GCF of 26 and 36 Examples

Example 1: The product of two numbers is 936. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 936
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 936/2
Therefore, the LCM is 468.
Example 2: For two numbers, GCF = 2 and LCM = 468. If one number is 26, find the other number.

Solution:

Given: GCF (z, 26) = 2 and LCM (z, 26) = 468
∵ GCF × LCM = 26 × (z)
⇒ z = (GCF × LCM)/26
⇒ z = (2 × 468)/26
⇒ z = 36
Therefore, the other number is 36.
Example 3: Find the GCF of 26 and 36, if their LCM is 468.

Solution:

∵ LCM × GCF = 26 × 36
⇒ GCF(26, 36) = (26 × 36)/468 = 2
Therefore, the greatest common factor of 26 and 36 is 2.

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FAQs on GCF of 26 and 36

What is the GCF of 26 and 36?

The GCF of 26 and 36 is 2. To calculate the GCF of 26 and 36, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 26 and 36, i.e., 2.

How to Find the GCF of 26 and 36 by Prime Factorization?

To find the GCF of 26 and 36, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 36 = 2 × 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 26 and 36. Hence, GCF (26, 36) = 2.
☛ Prime Number

What are the Methods to Find GCF of 26 and 36?

There are three commonly used methods to find the GCF of 26 and 36.

By Listing Common Factors
By Prime Factorization
By Long Division

If the GCF of 36 and 26 is 2, Find its LCM.

GCF(36, 26) × LCM(36, 26) = 36 × 26
Since the GCF of 36 and 26 = 2
⇒ 2 × LCM(36, 26) = 936
Therefore, LCM = 468
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How to Find the GCF of 26 and 36 by Long Division Method?

To find the GCF of 26, 36 using long division method, 36 is divided by 26. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 26, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 26 and 36, i.e. GCF × LCM = 26 × 36.

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