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GCF of 854/108, 521/214

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 854/108, 521/214 i.e 1/11556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/108, 521/214.

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 854/108,521/214?

Given fractions are 854/108,521/214

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 854/108,521/214, numerators are 854,521

Denominators are 108,214

The GCF of 854,521 is 1 .

LCM of 108,214 is 11556.

The greatest common factor of 854/108,521/214 = [GCF of 854,521]/[LCM of 108,214]= 1/11556

Therefore, the GCF of 854/108,521/214 is 1/11556.

Greatest Common Factor of 854,521

To find the highest common factor of 854,521, we have to find the factors of both numbers and list the highest common factor.

The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854

The factors of 521 are 1, 521

The HCF of 854,521 is 1.

Lets's calculate GCF of 854,521

Greatest Common Factor (GCF) of 854,521 By Common Division

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

Greatest Common Factor of 854,521 By Matching Biggest Common Factor Method

Greatest Common Factor of 854,521 By Matching Biggest Common Factor Method

Now, list down the factors of 854

:

1,2,7,14,61,122,427,854

Now, list down the factors of 521

:

1,521

Greatest Common Factor

We found the factors 854,521 . The biggest common factor number is the GCF number.
So the greatest common factor 854,521 is 1.

Lets's calculate LCM of 108,214

Lowest Common Multiple of 108,214 using Common Division

2 108, 214
54, 107

∴ So the LCM of the given numbers is 2 x 54 x 107 = 11556

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11556

Therefore, the GCF of Fractions 854/108,521/214 is 1/11556

Least Common Multiple of 108,214 with GCF Formula

Least Common Multiple of 108,214 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 108,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(108,214) = 2

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

GCF(108,214) x common factors =2 x 1 = 2

LCM(108,214) = ( 108 × 214 ) / 2

LCM(108,214) = 23112 / 2

LCM(108,214) = 11556


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FAQs on GCF of Fractions of 854/108, 521/214

1. What is the HCF of 854,521?

The HCF of 854,521 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 854/108, 521/214?

Answer: GCF of Numerators as per given numbers 854/108, 521/214 is

GCF of Numerators i.e. for 854,521 is 1

LCM of denominators i.e. for 108,214 is 11556.

Thus, GCF of Fractions is 1/11556.Finally, GCF of Fractions for 854/108, 521/214 is 1/11556.