Greatest Common Factor of 27/34, 277/40, 542/164

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 27/34, 277/40, 542/164

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 27/34,277/40,542/164

Given fractions are 27/34,277/40,542/164

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 27,277,542

Greatest Common Factor of Numerators i.e. GCF of 27,277,542 is 1 .

LCM of Denominators means LCM of 34,40,164 as per the given fractions.

LCM of 34,40,164 is 27880 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 27,277,542

GCF of Fractions 27/34,277/40,542/164 is 1/27880

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

Greatest Common Factor of 27,277,542 By Matching Biggest Common Factor Method

Greatest Common Factor of 27,277,542 By Matching Biggest Common Factor Method

Factors of 27

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

1,3,9,27

Factors of 277

List of positive integer factors of 277 that divides 277 without a remainder.

1,277

Factors of 542

List of positive integer factors of 542 that divides 542 without a remainder.

1,2,271,542

Greatest Common Factor

We found the factors 27,277,542 . The biggest common factor number is the GCF number.
So the greatest common factor 27,277,542 is 1.

Lets's calculate LCM of 34,40,164

2 34, 40, 164
2 17, 20, 82
17, 10, 41

∴ So the LCM of the given numbers is 2 x 2 x 17 x 10 x 41 = 27880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27880

Therefore, the GCF of Fractions 27/34,277/40,542/164 is 1/27880

Least Common Multiple of 34,40,164 with GCF Formula

Least Common Multiple of 34,40,164 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 34,40,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,40,164) = 2

common factors(in case of two or more numbers have common factors) = 4

GCF(34,40,164) x common factors =2 x 4 = 8

LCM(34,40,164) = ( 34 × 40 × 164 ) / 8

LCM(34,40,164) = 223040 / 8

LCM(34,40,164) = 27880


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 27/34, 277/40, 542/164

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 27/34, 277/40, 542/164?

Answer: GCF of Numerators as per given numbers 27/34, 277/40, 542/164 is

GCF of Numerators i.e. for 27,277,542 is 1

LCM of denominators i.e. for 34,40,164 is 27880.

Thus, GCF of Fractions is 1/27880.Finally, GCF of Fractions for 27/34, 277/40, 542/164 is 1/27880.