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GCF of 12 and 26

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

1.	GCF of 12 and 26
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 26?

Answer: GCF of 12 and 26 is 2.

Explanation:

The GCF of two non-zero integers, x(12) and y(26), is the greatest positive integer m(2) that divides both x(12) and y(26) without any remainder.

Methods to Find GCF of 12 and 26

The methods to find the GCF of 12 and 26 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 12 and 26 by Prime Factorization

Prime factorization of 12 and 26 is (2 × 2 × 3) and (2 × 13) respectively. As visible, 12 and 26 have only one common prime factor i.e. 2. Hence, the GCF of 12 and 26 is 2.

GCF of 12 and 26 by Long Division

GCF of 12 and 26 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 26 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 12 and 26.

GCF of 12 and 26 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 = 26 and Y = 12

GCF(26, 12) = GCF(12, 26 mod 12) = GCF(12, 2)
GCF(12, 2) = GCF(2, 12 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 26 is 2.

☛ Also Check:

GCF of 12 and 26 Examples

Example 1: The product of two numbers is 312. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 312
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 312/2
Therefore, the LCM is 156.
Example 2: Find the GCF of 12 and 26, if their LCM is 156.

Solution:

∵ LCM × GCF = 12 × 26
⇒ GCF(12, 26) = (12 × 26)/156 = 2
Therefore, the greatest common factor of 12 and 26 is 2.
Example 3: Find the greatest number that divides 12 and 26 exactly.

Solution:

The greatest number that divides 12 and 26 exactly is their greatest common factor, i.e. GCF of 12 and 26.
⇒ Factors of 12 and 26:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 26 = 1, 2, 13, 26
Therefore, the GCF of 12 and 26 is 2.

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FAQs on GCF of 12 and 26

What is the GCF of 12 and 26?

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

How to Find the GCF of 12 and 26 by Prime Factorization?

To find the GCF of 12 and 26, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 26 = 2 × 13.
⇒ Since 2 is the only common prime factor of 12 and 26. Hence, GCF (12, 26) = 2.
☛ Prime Numbers

How to Find the GCF of 12 and 26 by Long Division Method?

To find the GCF of 12, 26 using long division method, 26 is divided by 12. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 12, 26?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 26, i.e. GCF × LCM = 12 × 26.

What are the Methods to Find GCF of 12 and 26?

There are three commonly used methods to find the GCF of 12 and 26.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 26 and 12 is 2, Find its LCM.

GCF(26, 12) × LCM(26, 12) = 26 × 12
Since the GCF of 26 and 12 = 2
⇒ 2 × LCM(26, 12) = 312
Therefore, LCM = 156
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