How to Find GCF of 2178/516, 8363/404?

GCF of 2178/516, 8363/404

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 2178/516, 8363/404 i.e 1/52116 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2178/516, 8363/404.

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 2178/516,8363/404?

Given fractions are 2178/516,8363/404

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 2178/516,8363/404, numerators are 2178,8363

Denominators are 516,404

The GCF of 2178,8363 is 1 .

LCM of 516,404 is 52116.

The greatest common factor of 2178/516,8363/404 = [GCF of 2178,8363]/[LCM of 516,404]= 1/52116

Therefore, the GCF of 2178/516,8363/404 is 1/52116.

Greatest Common Factor of 2178,8363

To find the highest common factor of 2178,8363, we have to find the factors of both numbers and list the highest common factor.

The factors of 2178 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178

The factors of 8363 are 1, 8363

The HCF of 2178,8363 is 1.

Lets's calculate GCF of 2178,8363

Greatest Common Factor (GCF) of 2178,8363 By Common Division

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

Greatest Common Factor of 2178,8363 By Matching Biggest Common Factor Method

Now, list down the factors of 2178

1,2,3,6,9,11,18,22,33,66,99,121,198,242,363,726,1089,2178

Now, list down the factors of 8363

1,8363

Greatest Common Factor

We found the factors 2178,8363 . The biggest common factor number is the GCF number.
So the greatest common factor 2178,8363 is 1.

Lets's calculate LCM of 516,404

Lowest Common Multiple of 516,404 using Common Division

2	516, 404
2	258, 202
	129, 101

∴ So the LCM of the given numbers is 2 x 2 x 129 x 101 = 52116

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/52116

Therefore, the GCF of Fractions 2178/516,8363/404 is 1/52116

Least Common Multiple of 516,404 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 516,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(516,404) = 4

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

GCF(516,404) x common factors =4 x 1 = 4

LCM(516,404) = ( 516 × 404 ) / 4

LCM(516,404) = 208464 / 4

LCM(516,404) = 52116

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FAQs on GCF of Fractions of 2178/516, 8363/404

1. What is the HCF of 2178,8363?

The HCF of 2178,8363 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 2178/516, 8363/404?

Answer: GCF of Numerators as per given numbers 2178/516, 8363/404 is

GCF of Numerators i.e. for 2178,8363 is 1

LCM of denominators i.e. for 516,404 is 52116.

Thus, GCF of Fractions is 1/52116.Finally, GCF of Fractions for 2178/516, 8363/404 is 1/52116.