Greatest Common Factor of 54/30, 90/75, 108/180

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 54/30, 90/75, 108/180

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 54/30,90/75,108/180

Given fractions are 54/30,90/75,108/180

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 54,90,108

Greatest Common Factor of Numerators i.e. GCF of 54,90,108 is 18 .

LCM of Denominators means LCM of 30,75,180 as per the given fractions.

LCM of 30,75,180 is 900 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 54,90,108

GCF of Fractions 54/30,90/75,108/180 is 18/900

2 54, 90, 108
3 27, 45, 54
3 9, 15, 18
3, 5, 6

∴ So the GCF of the given numbers is 2 x 3 x 3 = 18

Greatest Common Factor of 54,90,108 By Matching Biggest Common Factor Method

Greatest Common Factor of 54,90,108 By Matching Biggest Common Factor Method

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1,2,3,6,9,18,27,54

Factors of 90

List of positive integer factors of 90 that divides 90 without a remainder.

1,2,3,5,6,9,10,15,18,30,45,90

Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,108

Greatest Common Factor

We found the factors 54,90,108 . The biggest common factor number is the GCF number.
So the greatest common factor 54,90,108 is 18.

Lets's calculate LCM of 30,75,180

2 30, 75, 180
3 15, 75, 90
5 5, 25, 30
1, 5, 6

∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 5 x 6 = 900

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/900

Therefore, the GCF of Fractions 54/30,90/75,108/180 is 18/900

Least Common Multiple of 30,75,180 with GCF Formula

Least Common Multiple of 30,75,180 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 30,75,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,75,180) = 15

common factors(in case of two or more numbers have common factors) = 30

GCF(30,75,180) x common factors =15 x 30 = 450

LCM(30,75,180) = ( 30 × 75 × 180 ) / 450

LCM(30,75,180) = 405000 / 450

LCM(30,75,180) = 900


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 54/30, 90/75, 108/180

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 54/30, 90/75, 108/180?

Answer: GCF of Numerators as per given numbers 54/30, 90/75, 108/180 is

GCF of Numerators i.e. for 54,90,108 is 18

LCM of denominators i.e. for 30,75,180 is 900.

Thus, GCF of Fractions is 18/900.Finally, GCF of Fractions for 54/30, 90/75, 108/180 is 18/900.