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GCF of 24 and 26

GCF of 24 and 26 is the largest possible number that divides 24 and 26 exactly without any remainder. The factors of 24 and 26 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 13, 26 respectively. There are 3 commonly used methods to find the GCF of 24 and 26 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 24 and 26
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 26?

Answer: GCF of 24 and 26 is 2.

Explanation:

The GCF of two non-zero integers, x(24) and y(26), is the greatest positive integer m(2) that divides both x(24) and y(26) without any remainder.

Methods to Find GCF of 24 and 26

The methods to find the GCF of 24 and 26 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 24 and 26 by Prime Factorization

Prime factorization of 24 and 26 is (2 × 2 × 2 × 3) and (2 × 13) respectively. As visible, 24 and 26 have only one common prime factor i.e. 2. Hence, the GCF of 24 and 26 is 2.

GCF of 24 and 26 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 26: 1, 2, 13, 26

There are 2 common factors of 24 and 26, that are 1 and 2. Therefore, the greatest common factor of 24 and 26 is 2.

GCF of 24 and 26 by Long Division

GCF of 24 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 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 24 and 26.

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GCF of 24 and 26 Examples

Example 1: Find the greatest number that divides 24 and 26 exactly.

Solution:

The greatest number that divides 24 and 26 exactly is their greatest common factor, i.e. GCF of 24 and 26.
⇒ Factors of 24 and 26:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 26 = 1, 2, 13, 26
Therefore, the GCF of 24 and 26 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 312. If one number is 24, find the other number.

Solution:

Given: GCF (z, 24) = 2 and LCM (z, 24) = 312
∵ GCF × LCM = 24 × (z)
⇒ z = (GCF × LCM)/24
⇒ z = (2 × 312)/24
⇒ z = 26
Therefore, the other number is 26.
Example 3: Find the GCF of 24 and 26, if their LCM is 312.

Solution:

∵ LCM × GCF = 24 × 26
⇒ GCF(24, 26) = (24 × 26)/312 = 2
Therefore, the greatest common factor of 24 and 26 is 2.

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FAQs on GCF of 24 and 26

What is the GCF of 24 and 26?

The GCF of 24 and 26 is 2. To calculate the GCF (Greatest Common Factor) of 24 and 26, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 26 = 1, 2, 13, 26) and choose the greatest factor that exactly divides both 24 and 26, i.e., 2.

What is the Relation Between LCM and GCF of 24, 26?

The following equation can be used to express the relation between Least Common Multiple and GCF of 24 and 26, i.e. GCF × LCM = 24 × 26.

If the GCF of 26 and 24 is 2, Find its LCM.

GCF(26, 24) × LCM(26, 24) = 26 × 24
Since the GCF of 26 and 24 = 2
⇒ 2 × LCM(26, 24) = 624
Therefore, LCM = 312
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What are the Methods to Find GCF of 24 and 26?

There are three commonly used methods to find the GCF of 24 and 26.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the GCF of 24 and 26 by Prime Factorization?

To find the GCF of 24 and 26, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 26 = 2 × 13.
⇒ Since 2 is the only common prime factor of 24 and 26. Hence, GCF (24, 26) = 2.
☛ What are Prime Numbers?

How to Find the GCF of 24 and 26 by Long Division Method?

To find the GCF of 24, 26 using long division method, 26 is divided by 24. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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