Greatest Common Factor of 538/84, 217/81, 306/71

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 538/84, 217/81, 306/71

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

Greatest Common Factor of 538/84,217/81,306/71

Given fractions are 538/84,217/81,306/71

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 538,217,306

Greatest Common Factor of Numerators i.e. GCF of 538,217,306 is 1 .

LCM of Denominators means LCM of 84,81,71 as per the given fractions.

LCM of 84,81,71 is 161028 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 538,217,306

GCF of Fractions 538/84,217/81,306/71 is 1/161028

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

Greatest Common Factor of 538,217,306 By Matching Biggest Common Factor Method

Greatest Common Factor of 538,217,306 By Matching Biggest Common Factor Method

Factors of 538

List of positive integer factors of 538 that divides 538 without a remainder.

1,2,269,538

Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1,7,31,217

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1,2,3,6,9,17,18,34,51,102,153,306

Greatest Common Factor

We found the factors 538,217,306 . The biggest common factor number is the GCF number.
So the greatest common factor 538,217,306 is 1.

Lets's calculate LCM of 84,81,71

3 84, 81, 71
28, 27, 71

∴ So the LCM of the given numbers is 3 x 28 x 27 x 71 = 161028

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/161028

Therefore, the GCF of Fractions 538/84,217/81,306/71 is 1/161028

Least Common Multiple of 84,81,71 with GCF Formula

Least Common Multiple of 84,81,71 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 84,81,71 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(84,81,71) = 1

common factors(in case of two or more numbers have common factors) = 3

GCF(84,81,71) x common factors =1 x 3 = 3

LCM(84,81,71) = ( 84 × 81 × 71 ) / 3

LCM(84,81,71) = 483084 / 3

LCM(84,81,71) = 161028


GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 538/84, 217/81, 306/71

1. 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.

2. What is the GCF of Fractions for 538/84, 217/81, 306/71?

Answer: GCF of Numerators as per given numbers 538/84, 217/81, 306/71 is

GCF of Numerators i.e. for 538,217,306 is 1

LCM of denominators i.e. for 84,81,71 is 161028.

Thus, GCF of Fractions is 1/161028.Finally, GCF of Fractions for 538/84, 217/81, 306/71 is 1/161028.