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GCF of 26 and 14

GCF of 26 and 14 is the largest possible number that divides 26 and 14 exactly without any remainder. The factors of 26 and 14 are 1, 2, 13, 26 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 26 and 14 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 26 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 14?

Answer: GCF of 26 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(26) and y(14), is the greatest positive integer m(2) that divides both x(26) and y(14) without any remainder.

Methods to Find GCF of 26 and 14

Let's look at the different methods for finding the GCF of 26 and 14.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 26 and 14 by Prime Factorization

Prime factorization of 26 and 14 is (2 × 13) and (2 × 7) respectively. As visible, 26 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 26 and 14 is 2.

GCF of 26 and 14 by Listing Common Factors

Factors of 26: 1, 2, 13, 26
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 26 and 14, that are 1 and 2. Therefore, the greatest common factor of 26 and 14 is 2.

GCF of 26 and 14 by Long Division

GCF of 26 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 26 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 26 and 14.

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GCF of 26 and 14 Examples

Example 1: Find the greatest number that divides 26 and 14 exactly.

Solution:

The greatest number that divides 26 and 14 exactly is their greatest common factor, i.e. GCF of 26 and 14.
⇒ Factors of 26 and 14:
- Factors of 26 = 1, 2, 13, 26
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 26 and 14 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 182. If one number is 26, find the other number.

Solution:

Given: GCF (y, 26) = 2 and LCM (y, 26) = 182
∵ GCF × LCM = 26 × (y)
⇒ y = (GCF × LCM)/26
⇒ y = (2 × 182)/26
⇒ y = 14
Therefore, the other number is 14.
Example 3: The product of two numbers is 364. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 364
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 364/2
Therefore, the LCM is 182.

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FAQs on GCF of 26 and 14

What is the GCF of 26 and 14?

The GCF of 26 and 14 is 2. To calculate the greatest common factor (GCF) of 26 and 14, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 26 and 14, i.e., 2.

If the GCF of 14 and 26 is 2, Find its LCM.

GCF(14, 26) × LCM(14, 26) = 14 × 26
Since the GCF of 14 and 26 = 2
⇒ 2 × LCM(14, 26) = 364
Therefore, LCM = 182
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 26, 14?

The following equation can be used to express the relation between LCM and GCF of 26 and 14, i.e. GCF × LCM = 26 × 14.

How to Find the GCF of 26 and 14 by Prime Factorization?

To find the GCF of 26 and 14, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 26 and 14. Hence, GCF (26, 14) = 2.
☛ Prime Number

How to Find the GCF of 26 and 14 by Long Division Method?

To find the GCF of 26, 14 using long division method, 26 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 26 and 14?

There are three commonly used methods to find the GCF of 26 and 14.

By Long Division
By Prime Factorization
By Listing Common Factors

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