A day full of math games & activities. Find one near you.

GCF of 26 and 34

GCF of 26 and 34 is the largest possible number that divides 26 and 34 exactly without any remainder. The factors of 26 and 34 are 1, 2, 13, 26 and 1, 2, 17, 34 respectively. There are 3 commonly used methods to find the GCF of 26 and 34 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 26 and 34
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 26 and 34?

Answer: GCF of 26 and 34 is 2.

Explanation:

The GCF of two non-zero integers, x(26) and y(34), is the greatest positive integer m(2) that divides both x(26) and y(34) without any remainder.

Methods to Find GCF of 26 and 34

The methods to find the GCF of 26 and 34 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 26 and 34 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 = 34 and Y = 26

GCF(34, 26) = GCF(26, 34 mod 26) = GCF(26, 8)
GCF(26, 8) = GCF(8, 26 mod 8) = GCF(8, 2)
GCF(8, 2) = GCF(2, 8 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 26 and 34 is 2.

GCF of 26 and 34 by Long Division

GCF of 26 and 34 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 34 (larger number) by 26 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (26) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 26 and 34.

GCF of 26 and 34 by Prime Factorization

Prime factorization of 26 and 34 is (2 × 13) and (2 × 17) respectively. As visible, 26 and 34 have only one common prime factor i.e. 2. Hence, the GCF of 26 and 34 is 2.

☛ Also Check:

GCF of 26 and 34 Examples

Example 1: The product of two numbers is 884. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 884
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 884/2
Therefore, the LCM is 442.
Example 2: Find the greatest number that divides 26 and 34 exactly.

Solution:

The greatest number that divides 26 and 34 exactly is their greatest common factor, i.e. GCF of 26 and 34.
⇒ Factors of 26 and 34:
- Factors of 26 = 1, 2, 13, 26
- Factors of 34 = 1, 2, 17, 34
Therefore, the GCF of 26 and 34 is 2.
Example 3: Find the GCF of 26 and 34, if their LCM is 442.

Solution:

∵ LCM × GCF = 26 × 34
⇒ GCF(26, 34) = (26 × 34)/442 = 2
Therefore, the greatest common factor of 26 and 34 is 2.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 26 and 34

What is the GCF of 26 and 34?

The GCF of 26 and 34 is 2. To calculate the greatest common factor of 26 and 34, we need to factor each number (factors of 26 = 1, 2, 13, 26; factors of 34 = 1, 2, 17, 34) and choose the greatest factor that exactly divides both 26 and 34, i.e., 2.

What is the Relation Between LCM and GCF of 26, 34?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 26 and 34, i.e. GCF × LCM = 26 × 34.

If the GCF of 34 and 26 is 2, Find its LCM.

GCF(34, 26) × LCM(34, 26) = 34 × 26
Since the GCF of 34 and 26 = 2
⇒ 2 × LCM(34, 26) = 884
Therefore, LCM = 442
☛ Greatest Common Factor Calculator

How to Find the GCF of 26 and 34 by Prime Factorization?

To find the GCF of 26 and 34, we will find the prime factorization of the given numbers, i.e. 26 = 2 × 13; 34 = 2 × 17.
⇒ Since 2 is the only common prime factor of 26 and 34. Hence, GCF (26, 34) = 2.
☛ What is a Prime Number?

What are the Methods to Find GCF of 26 and 34?

There are three commonly used methods to find the GCF of 26 and 34.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 26 and 34 by Long Division Method?

To find the GCF of 26, 34 using long division method, 34 is divided by 26. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum