Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 20/82,85/76,10/24,78/20
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 20,85,10,78
Greatest Common Factor of Numerators i.e. GCF of 20,85,10,78 is 1 .
LCM of Denominators means LCM of 82,76,24,20 as per the given fractions.
LCM of 82,76,24,20 is 93480 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 20,85,10,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 85
List of positive integer factors of 85 that divides 85 without a remainder.
1,5,17,85
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
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 20,85,10,78 . The biggest common factor number is the GCF number.
So the greatest common factor 20,85,10,78 is 1.
Lets's calculate LCM of 82,76,24,20
2 | 82, 76, 24, 20 |
2 | 41, 38, 12, 10 |
41, 19, 6, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 41 x 19 x 6 x 5 = 93480
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/93480
Therefore, the GCF of Fractions 20/82,85/76,10/24,78/20 is 1/93480
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 82,76,24,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,76,24,20) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(82,76,24,20) x common factors =2 x 16 = 32
LCM(82,76,24,20) = ( 82 × 76 × 24 × 20 ) / 32
LCM(82,76,24,20) = 2991360 / 32
LCM(82,76,24,20) = 93480
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 20/82, 85/76, 10/24, 78/20?
Answer: GCF of Numerators as per given numbers 20/82, 85/76, 10/24, 78/20 is
GCF of Numerators i.e. for 20,85,10,78 is 1
LCM of denominators i.e. for 82,76,24,20 is 93480.
Thus, GCF of Fractions is 1/93480.Finally, GCF of Fractions for 20/82, 85/76, 10/24, 78/20 is 1/93480.