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GCF of 891/214, 314/870

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 891/214, 314/870 i.e 1/93090 easily. The following is the detailed procedure to determine the greatest common factor of fractions 891/214, 314/870.

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 891/214,314/870?

Given fractions are 891/214,314/870

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 891/214,314/870, numerators are 891,314

Denominators are 214,870

The GCF of 891,314 is 1 .

LCM of 214,870 is 93090.

The greatest common factor of 891/214,314/870 = [GCF of 891,314]/[LCM of 214,870]= 1/93090

Therefore, the GCF of 891/214,314/870 is 1/93090.

Greatest Common Factor of 891,314

To find the highest common factor of 891,314, we have to find the factors of both numbers and list the highest common factor.

The factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, 891

The factors of 314 are 1, 2, 157, 314

The HCF of 891,314 is 1.

Lets's calculate GCF of 891,314

Greatest Common Factor (GCF) of 891,314 By Common Division

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

Greatest Common Factor of 891,314 By Matching Biggest Common Factor Method

Greatest Common Factor of 891,314 By Matching Biggest Common Factor Method

Now, list down the factors of 891

:

1,3,9,11,27,33,81,99,297,891

Now, list down the factors of 314

:

1,2,157,314

Greatest Common Factor

We found the factors 891,314 . The biggest common factor number is the GCF number.
So the greatest common factor 891,314 is 1.

Lets's calculate LCM of 214,870

Lowest Common Multiple of 214,870 using Common Division

2 214, 870
107, 435

∴ So the LCM of the given numbers is 2 x 107 x 435 = 93090

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93090

Therefore, the GCF of Fractions 891/214,314/870 is 1/93090

Least Common Multiple of 214,870 with GCF Formula

Least Common Multiple of 214,870 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 214,870 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,870) = 2

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

GCF(214,870) x common factors =2 x 1 = 2

LCM(214,870) = ( 214 × 870 ) / 2

LCM(214,870) = 186180 / 2

LCM(214,870) = 93090


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FAQs on GCF of Fractions of 891/214, 314/870

1. What is the HCF of 891,314?

The HCF of 891,314 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 891/214, 314/870?

Answer: GCF of Numerators as per given numbers 891/214, 314/870 is

GCF of Numerators i.e. for 891,314 is 1

LCM of denominators i.e. for 214,870 is 93090.

Thus, GCF of Fractions is 1/93090.Finally, GCF of Fractions for 891/214, 314/870 is 1/93090.