Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
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
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
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
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
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
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.