How to Find GCF of 6378/213, 8178/4891?

GCF of 6378/213, 8178/4891

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 6378/213, 8178/4891 i.e 6/1041783 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6378/213, 8178/4891.

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 6378/213,8178/4891?

Given fractions are 6378/213,8178/4891

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 6378/213,8178/4891, numerators are 6378,8178

Denominators are 213,4891

The GCF of 6378,8178 is 6 .

LCM of 213,4891 is 1041783.

The greatest common factor of 6378/213,8178/4891 = [GCF of 6378,8178]/[LCM of 213,4891]= 6/1041783

Therefore, the GCF of 6378/213,8178/4891 is 6/1041783.

Greatest Common Factor of 6378,8178

To find the highest common factor of 6378,8178, we have to find the factors of both numbers and list the highest common factor.

The factors of 6378 are 1, 2, 3, 6, 1063, 2126, 3189, 6378

The factors of 8178 are 1, 2, 3, 6, 29, 47, 58, 87, 94, 141, 174, 282, 1363, 2726, 4089, 8178

The HCF of 6378,8178 is 6.

Lets's calculate GCF of 6378,8178

Greatest Common Factor (GCF) of 6378,8178 By Common Division

2	6378, 8178
3	3189, 4089
	1063, 1363

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 6378,8178 By Matching Biggest Common Factor Method

Now, list down the factors of 6378

1,2,3,6,1063,2126,3189,6378

Now, list down the factors of 8178

1,2,3,6,29,47,58,87,94,141,174,282,1363,2726,4089,8178

Greatest Common Factor

We found the factors 6378,8178 . The biggest common factor number is the GCF number.
So the greatest common factor 6378,8178 is 6.

Lets's calculate LCM of 213,4891

Lowest Common Multiple of 213,4891 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1041783

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1041783

Therefore, the GCF of Fractions 6378/213,8178/4891 is 6/1041783

Least Common Multiple of 213,4891 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 213,4891 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(213,4891) = 1

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

GCF(213,4891) x common factors =1 x 1 = 1

LCM(213,4891) = ( 213 × 4891 ) / 1

LCM(213,4891) = 1041783 / 1

LCM(213,4891) = 1041783

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FAQs on GCF of Fractions of 6378/213, 8178/4891

1. What is the HCF of 6378,8178?

The HCF of 6378,8178 is 6

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 6378/213, 8178/4891?

Answer: GCF of Numerators as per given numbers 6378/213, 8178/4891 is

GCF of Numerators i.e. for 6378,8178 is 6

LCM of denominators i.e. for 213,4891 is 1041783.

Thus, GCF of Fractions is 6/1041783.Finally, GCF of Fractions for 6378/213, 8178/4891 is 6/1041783.