How to Find GCF of 260/337, 380/872?

GCF of 260/337, 380/872

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 260/337, 380/872 i.e 20/293864 easily. The following is the detailed procedure to determine the greatest common factor of fractions 260/337, 380/872.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 260/337,380/872?

Given fractions are 260/337,380/872

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 260/337,380/872, numerators are 260,380

Denominators are 337,872

The GCF of 260,380 is 20 .

LCM of 337,872 is 293864.

The greatest common factor of 260/337,380/872 = [GCF of 260,380]/[LCM of 337,872]= 20/293864

Therefore, the GCF of 260/337,380/872 is 20/293864.

Greatest Common Factor of 260,380

To find the highest common factor of 260,380, we have to find the factors of both numbers and list the highest common factor.

The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The HCF of 260,380 is 20.

Lets's calculate GCF of 260,380

Greatest Common Factor (GCF) of 260,380 By Common Division

2	260, 380
2	130, 190
5	65, 95
	13, 19

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 260,380 By Matching Biggest Common Factor Method

Now, list down the factors of 260

1,2,4,5,10,13,20,26,52,65,130,260

Now, list down the factors of 380

1,2,4,5,10,19,20,38,76,95,190,380

Greatest Common Factor

We found the factors 260,380 . The biggest common factor number is the GCF number.
So the greatest common factor 260,380 is 20.

Lets's calculate LCM of 337,872

Lowest Common Multiple of 337,872 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 293864

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/293864

Therefore, the GCF of Fractions 260/337,380/872 is 20/293864

Least Common Multiple of 337,872 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 337,872 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(337,872) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(337,872) x common factors =1 x 1 = 1

LCM(337,872) = ( 337 × 872 ) / 1

LCM(337,872) = 293864 / 1

LCM(337,872) = 293864

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FAQs on GCF of Fractions of 260/337, 380/872

1. What is the HCF of 260,380?

The HCF of 260,380 is 20

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 260/337, 380/872?

Answer: GCF of Numerators as per given numbers 260/337, 380/872 is

GCF of Numerators i.e. for 260,380 is 20

LCM of denominators i.e. for 337,872 is 293864.

Thus, GCF of Fractions is 20/293864.Finally, GCF of Fractions for 260/337, 380/872 is 20/293864.