Greatest Common Factor of 144/144, 180/180, 300/198

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

GCF of 144/144, 180/180, 300/198

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 144/144,180/180,300/198

Given fractions are 144/144,180/180,300/198

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 144,180,300

Greatest Common Factor of Numerators i.e. GCF of 144,180,300 is 12 .

LCM of Denominators means LCM of 144,180,198 as per the given fractions.

LCM of 144,180,198 is 7920 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 144,180,300

GCF of Fractions 144/144,180/180,300/198 is 12/7920

2 144, 180, 300
2 72, 90, 150
3 36, 45, 75
12, 15, 25

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 144,180,300 By Matching Biggest Common Factor Method

Greatest Common Factor of 144,180,300 By Matching Biggest Common Factor Method

Factors of 144

List of positive integer factors of 144 that divides 144 without a remainder.

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Factors of 180

List of positive integer factors of 180 that divides 180 without a remainder.

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300

Greatest Common Factor

We found the factors 144,180,300 . The biggest common factor number is the GCF number.
So the greatest common factor 144,180,300 is 12.

Lets's calculate LCM of 144,180,198

2 144, 180, 198
2 72, 90, 99
3 36, 45, 99
3 12, 15, 33
4, 5, 11

∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 4 x 5 x 11 = 7920

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/7920

Therefore, the GCF of Fractions 144/144,180/180,300/198 is 12/7920

Least Common Multiple of 144,180,198 with GCF Formula

Least Common Multiple of 144,180,198 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 144,180,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(144,180,198) = 18

common factors(in case of two or more numbers have common factors) = 36

GCF(144,180,198) x common factors =18 x 36 = 648

LCM(144,180,198) = ( 144 × 180 × 198 ) / 648

LCM(144,180,198) = 5132160 / 648

LCM(144,180,198) = 7920


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 144/144, 180/180, 300/198

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 144/144, 180/180, 300/198?

Answer: GCF of Numerators as per given numbers 144/144, 180/180, 300/198 is

GCF of Numerators i.e. for 144,180,300 is 12

LCM of denominators i.e. for 144,180,198 is 7920.

Thus, GCF of Fractions is 12/7920.Finally, GCF of Fractions for 144/144, 180/180, 300/198 is 12/7920.