How to Find GCF of 854/400, 5820/677?

GCF of 854/400, 5820/677

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 854/400, 5820/677 i.e 2/270800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/400, 5820/677.

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 854/400,5820/677?

Given fractions are 854/400,5820/677

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 854/400,5820/677, numerators are 854,5820

Denominators are 400,677

The GCF of 854,5820 is 2 .

LCM of 400,677 is 270800.

The greatest common factor of 854/400,5820/677 = [GCF of 854,5820]/[LCM of 400,677]= 2/270800

Therefore, the GCF of 854/400,5820/677 is 2/270800.

Greatest Common Factor of 854,5820

To find the highest common factor of 854,5820, 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 5820 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 97, 194, 291, 388, 485, 582, 970, 1164, 1455, 1940, 2910, 5820

The HCF of 854,5820 is 2.

Lets's calculate GCF of 854,5820

Greatest Common Factor (GCF) of 854,5820 By Common Division

2	854, 5820
	427, 2910

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

Greatest Common Factor of 854,5820 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 5820

1,2,3,4,5,6,10,12,15,20,30,60,97,194,291,388,485,582,970,1164,1455,1940,2910,5820

Greatest Common Factor

We found the factors 854,5820 . The biggest common factor number is the GCF number.
So the greatest common factor 854,5820 is 2.

Lets's calculate LCM of 400,677

Lowest Common Multiple of 400,677 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 270800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/270800

Therefore, the GCF of Fractions 854/400,5820/677 is 2/270800

Least Common Multiple of 400,677 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 400,677 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(400,677) = 1

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

GCF(400,677) x common factors =1 x 1 = 1

LCM(400,677) = ( 400 × 677 ) / 1

LCM(400,677) = 270800 / 1

LCM(400,677) = 270800

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FAQs on GCF of Fractions of 854/400, 5820/677

1. What is the HCF of 854,5820?

The HCF of 854,5820 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 854/400, 5820/677?

Answer: GCF of Numerators as per given numbers 854/400, 5820/677 is

GCF of Numerators i.e. for 854,5820 is 2

LCM of denominators i.e. for 400,677 is 270800.

Thus, GCF of Fractions is 2/270800.Finally, GCF of Fractions for 854/400, 5820/677 is 2/270800.