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GCF of 677/86, 422/109

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 677/86, 422/109 i.e 1/9374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 677/86, 422/109.

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 677/86,422/109?

Given fractions are 677/86,422/109

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 677/86,422/109, numerators are 677,422

Denominators are 86,109

The GCF of 677,422 is 1 .

LCM of 86,109 is 9374.

The greatest common factor of 677/86,422/109 = [GCF of 677,422]/[LCM of 86,109]= 1/9374

Therefore, the GCF of 677/86,422/109 is 1/9374.

Greatest Common Factor of 677,422

To find the highest common factor of 677,422, we have to find the factors of both numbers and list the highest common factor.

The factors of 677 are 1, 677

The factors of 422 are 1, 2, 211, 422

The HCF of 677,422 is 1.

Lets's calculate GCF of 677,422

Greatest Common Factor (GCF) of 677,422 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 677,422 By Matching Biggest Common Factor Method

Greatest Common Factor of 677,422 By Matching Biggest Common Factor Method

Now, list down the factors of 677

:

1,677

Now, list down the factors of 422

:

1,2,211,422

Greatest Common Factor

We found the factors 677,422 . The biggest common factor number is the GCF number.
So the greatest common factor 677,422 is 1.

Lets's calculate LCM of 86,109

Lowest Common Multiple of 86,109 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9374

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9374

Therefore, the GCF of Fractions 677/86,422/109 is 1/9374

Least Common Multiple of 86,109 with GCF Formula

Least Common Multiple of 86,109 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 86,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(86,109) = 1

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

GCF(86,109) x common factors =1 x 1 = 1

LCM(86,109) = ( 86 × 109 ) / 1

LCM(86,109) = 9374 / 1

LCM(86,109) = 9374


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FAQs on GCF of Fractions of 677/86, 422/109

1. What is the HCF of 677,422?

The HCF of 677,422 is 1

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 677/86, 422/109?

Answer: GCF of Numerators as per given numbers 677/86, 422/109 is

GCF of Numerators i.e. for 677,422 is 1

LCM of denominators i.e. for 86,109 is 9374.

Thus, GCF of Fractions is 1/9374.Finally, GCF of Fractions for 677/86, 422/109 is 1/9374.