Greatest Common Factor of 82/68, 77/12, 14/270

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 82/68, 77/12, 14/270

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 82/68,77/12,14/270

Given fractions are 82/68,77/12,14/270

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 82,77,14

Greatest Common Factor of Numerators i.e. GCF of 82,77,14 is 1 .

LCM of Denominators means LCM of 68,12,270 as per the given fractions.

LCM of 68,12,270 is 9180 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 82,77,14

GCF of Fractions 82/68,77/12,14/270 is 1/9180

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

Greatest Common Factor of 82,77,14 By Matching Biggest Common Factor Method

Greatest Common Factor of 82,77,14 By Matching Biggest Common Factor Method

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1,7,11,77

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Greatest Common Factor

We found the factors 82,77,14 . The biggest common factor number is the GCF number.
So the greatest common factor 82,77,14 is 1.

Lets's calculate LCM of 68,12,270

2 68, 12, 270
2 34, 6, 135
3 17, 3, 135
17, 1, 45

∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 1 x 45 = 9180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9180

Therefore, the GCF of Fractions 82/68,77/12,14/270 is 1/9180

Least Common Multiple of 68,12,270 with GCF Formula

Least Common Multiple of 68,12,270 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 68,12,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(68,12,270) = 2

common factors(in case of two or more numbers have common factors) = 12

GCF(68,12,270) x common factors =2 x 12 = 24

LCM(68,12,270) = ( 68 × 12 × 270 ) / 24

LCM(68,12,270) = 220320 / 24

LCM(68,12,270) = 9180


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 82/68, 77/12, 14/270

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 82/68, 77/12, 14/270?

Answer: GCF of Numerators as per given numbers 82/68, 77/12, 14/270 is

GCF of Numerators i.e. for 82,77,14 is 1

LCM of denominators i.e. for 68,12,270 is 9180.

Thus, GCF of Fractions is 1/9180.Finally, GCF of Fractions for 82/68, 77/12, 14/270 is 1/9180.