Greatest Common Factor of 69/20, 27/85, 102/109

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 69/20, 27/85, 102/109

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 69/20,27/85,102/109

Given fractions are 69/20,27/85,102/109

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 69,27,102

Greatest Common Factor of Numerators i.e. GCF of 69,27,102 is 3 .

LCM of Denominators means LCM of 20,85,109 as per the given fractions.

LCM of 20,85,109 is 37060 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 69,27,102

GCF of Fractions 69/20,27/85,102/109 is 3/37060

3 69, 27, 102
23, 9, 34

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 69,27,102 By Matching Biggest Common Factor Method

Greatest Common Factor of 69,27,102 By Matching Biggest Common Factor Method

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1,3,23,69

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1,3,9,27

Factors of 102

List of positive integer factors of 102 that divides 102 without a remainder.

1,2,3,6,17,34,51,102

Greatest Common Factor

We found the factors 69,27,102 . The biggest common factor number is the GCF number.
So the greatest common factor 69,27,102 is 3.

Lets's calculate LCM of 20,85,109

5 20, 85, 109
4, 17, 109

∴ So the LCM of the given numbers is 5 x 4 x 17 x 109 = 37060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/37060

Therefore, the GCF of Fractions 69/20,27/85,102/109 is 3/37060

Least Common Multiple of 20,85,109 with GCF Formula

Least Common Multiple of 20,85,109 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 20,85,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,85,109) = 1

common factors(in case of two or more numbers have common factors) = 5

GCF(20,85,109) x common factors =1 x 5 = 5

LCM(20,85,109) = ( 20 × 85 × 109 ) / 5

LCM(20,85,109) = 185300 / 5

LCM(20,85,109) = 37060


GCF of Fractions Calculation Examples

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GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

Frequently Asked Questions on Fractional GCF of 69/20, 27/85, 102/109

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 69/20, 27/85, 102/109?

Answer: GCF of Numerators as per given numbers 69/20, 27/85, 102/109 is

GCF of Numerators i.e. for 69,27,102 is 3

LCM of denominators i.e. for 20,85,109 is 37060.

Thus, GCF of Fractions is 3/37060.Finally, GCF of Fractions for 69/20, 27/85, 102/109 is 3/37060.