Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/60,81/50,96/76,30/18
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 9,81,96,30
Greatest Common Factor of Numerators i.e. GCF of 9,81,96,30 is 3 .
LCM of Denominators means LCM of 60,50,76,18 as per the given fractions.
LCM of 60,50,76,18 is 17100 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 9,81,96,30
3 | 9, 81, 96, 30 |
3, 27, 32, 10 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors 9,81,96,30 . The biggest common factor number is the GCF number.
So the greatest common factor 9,81,96,30 is 3.
Lets's calculate LCM of 60,50,76,18
2 | 60, 50, 76, 18 |
2 | 30, 25, 38, 9 |
3 | 15, 25, 19, 9 |
5 | 5, 25, 19, 3 |
1, 5, 19, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 5 x 19 x 3 = 17100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/17100
Therefore, the GCF of Fractions 9/60,81/50,96/76,30/18 is 3/17100
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 60,50,76,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,50,76,18) = 2
common factors(in case of two or more numbers have common factors) = 120
GCF(60,50,76,18) x common factors =2 x 120 = 240
LCM(60,50,76,18) = ( 60 × 50 × 76 × 18 ) / 240
LCM(60,50,76,18) = 4104000 / 240
LCM(60,50,76,18) = 17100
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 9/60, 81/50, 96/76, 30/18?
Answer: GCF of Numerators as per given numbers 9/60, 81/50, 96/76, 30/18 is
GCF of Numerators i.e. for 9,81,96,30 is 3
LCM of denominators i.e. for 60,50,76,18 is 17100.
Thus, GCF of Fractions is 3/17100.Finally, GCF of Fractions for 9/60, 81/50, 96/76, 30/18 is 3/17100.