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GCF of 976/305, 2686/419

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 976/305, 2686/419 i.e 2/127795 easily. The following is the detailed procedure to determine the greatest common factor of fractions 976/305, 2686/419.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 976/305,2686/419?

Given fractions are 976/305,2686/419

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 976/305,2686/419, numerators are 976,2686

Denominators are 305,419

The GCF of 976,2686 is 2 .

LCM of 305,419 is 127795.

The greatest common factor of 976/305,2686/419 = [GCF of 976,2686]/[LCM of 305,419]= 2/127795

Therefore, the GCF of 976/305,2686/419 is 2/127795.

Greatest Common Factor of 976,2686

To find the highest common factor of 976,2686, we have to find the factors of both numbers and list the highest common factor.

The factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976

The factors of 2686 are 1, 2, 17, 34, 79, 158, 1343, 2686

The HCF of 976,2686 is 2.

Lets's calculate GCF of 976,2686

Greatest Common Factor (GCF) of 976,2686 By Common Division

2 976, 2686
488, 1343

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 976,2686 By Matching Biggest Common Factor Method

Greatest Common Factor of 976,2686 By Matching Biggest Common Factor Method

Now, list down the factors of 976

:

1,2,4,8,16,61,122,244,488,976

Now, list down the factors of 2686

:

1,2,17,34,79,158,1343,2686

Greatest Common Factor

We found the factors 976,2686 . The biggest common factor number is the GCF number.
So the greatest common factor 976,2686 is 2.

Lets's calculate LCM of 305,419

Lowest Common Multiple of 305,419 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 127795

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/127795

Therefore, the GCF of Fractions 976/305,2686/419 is 2/127795

Least Common Multiple of 305,419 with GCF Formula

Least Common Multiple of 305,419 with GCF Formula

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

We need to calculate greatest common factor of 305,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(305,419) = 1

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

GCF(305,419) x common factors =1 x 1 = 1

LCM(305,419) = ( 305 × 419 ) / 1

LCM(305,419) = 127795 / 1

LCM(305,419) = 127795


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FAQs on GCF of Fractions of 976/305, 2686/419

1. What is the HCF of 976,2686?

The HCF of 976,2686 is 2

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 976/305, 2686/419?

Answer: GCF of Numerators as per given numbers 976/305, 2686/419 is

GCF of Numerators i.e. for 976,2686 is 2

LCM of denominators i.e. for 305,419 is 127795.

Thus, GCF of Fractions is 2/127795.Finally, GCF of Fractions for 976/305, 2686/419 is 2/127795.