Greatest Common Factor of 27/51, 45/60, 978/13

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 27/51, 45/60, 978/13

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 27/51,45/60,978/13

Given fractions are 27/51,45/60,978/13

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 27,45,978

Greatest Common Factor of Numerators i.e. GCF of 27,45,978 is 3 .

LCM of Denominators means LCM of 51,60,13 as per the given fractions.

LCM of 51,60,13 is 13260 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 27,45,978

GCF of Fractions 27/51,45/60,978/13 is 3/13260

3 27, 45, 978
9, 15, 326

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

Greatest Common Factor of 27,45,978 By Matching Biggest Common Factor Method

Greatest Common Factor of 27,45,978 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 45

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

Factors of 978

List of positive integer factors of 978 that divides 978 without a remainder.

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 27,45,978 . The biggest common factor number is the GCF number.
So the greatest common factor 27,45,978 is 3.

Lets's calculate LCM of 51,60,13

3 51, 60, 13
17, 20, 13

∴ So the LCM of the given numbers is 3 x 17 x 20 x 13 = 13260

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/13260

Therefore, the GCF of Fractions 27/51,45/60,978/13 is 3/13260

Least Common Multiple of 51,60,13 with GCF Formula

Least Common Multiple of 51,60,13 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 51,60,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(51,60,13) = 1

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

GCF(51,60,13) x common factors =1 x 3 = 3

LCM(51,60,13) = ( 51 × 60 × 13 ) / 3

LCM(51,60,13) = 39780 / 3

LCM(51,60,13) = 13260


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 27/51, 45/60, 978/13

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 27/51, 45/60, 978/13?

Answer: GCF of Numerators as per given numbers 27/51, 45/60, 978/13 is

GCF of Numerators i.e. for 27,45,978 is 3

LCM of denominators i.e. for 51,60,13 is 13260.

Thus, GCF of Fractions is 3/13260.Finally, GCF of Fractions for 27/51, 45/60, 978/13 is 3/13260.