Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/20,82/91,54/13,78/61
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 96,82,54,78
Greatest Common Factor of Numerators i.e. GCF of 96,82,54,78 is 2 .
LCM of Denominators means LCM of 20,91,13,61 as per the given fractions.
LCM of 20,91,13,61 is 111020 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 96,82,54,78
2 | 96, 82, 54, 78 |
48, 41, 27, 39 |
∴ So the GCF of the given numbers is 2 = 2
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 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
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 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 96,82,54,78 . The biggest common factor number is the GCF number.
So the greatest common factor 96,82,54,78 is 2.
Lets's calculate LCM of 20,91,13,61
13 | 20, 91, 13, 61 |
20, 7, 1, 61 |
∴ So the LCM of the given numbers is 13 x 20 x 7 x 1 x 61 = 111020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/111020
Therefore, the GCF of Fractions 96/20,82/91,54/13,78/61 is 2/111020
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 20,91,13,61 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,91,13,61) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(20,91,13,61) x common factors =1 x 13 = 13
LCM(20,91,13,61) = ( 20 × 91 × 13 × 61 ) / 13
LCM(20,91,13,61) = 1443260 / 13
LCM(20,91,13,61) = 111020
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 96/20, 82/91, 54/13, 78/61?
Answer: GCF of Numerators as per given numbers 96/20, 82/91, 54/13, 78/61 is
GCF of Numerators i.e. for 96,82,54,78 is 2
LCM of denominators i.e. for 20,91,13,61 is 111020.
Thus, GCF of Fractions is 2/111020.Finally, GCF of Fractions for 96/20, 82/91, 54/13, 78/61 is 2/111020.