Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/21,80/51,20/86
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 82,80,20
Greatest Common Factor of Numerators i.e. GCF of 82,80,20 is 2 .
LCM of Denominators means LCM of 21,51,86 as per the given fractions.
LCM of 21,51,86 is 30702 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 82,80,20
2 | 82, 80, 20 |
41, 40, 10 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Greatest Common Factor
We found the factors 82,80,20 . The biggest common factor number is the GCF number.
So the greatest common factor 82,80,20 is 2.
Lets's calculate LCM of 21,51,86
3 | 21, 51, 86 |
7, 17, 86 |
∴ So the LCM of the given numbers is 3 x 7 x 17 x 86 = 30702
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30702
Therefore, the GCF of Fractions 82/21,80/51,20/86 is 2/30702
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 21,51,86 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,51,86) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(21,51,86) x common factors =1 x 3 = 3
LCM(21,51,86) = ( 21 × 51 × 86 ) / 3
LCM(21,51,86) = 92106 / 3
LCM(21,51,86) = 30702
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 82/21, 80/51, 20/86?
Answer: GCF of Numerators as per given numbers 82/21, 80/51, 20/86 is
GCF of Numerators i.e. for 82,80,20 is 2
LCM of denominators i.e. for 21,51,86 is 30702.
Thus, GCF of Fractions is 2/30702.Finally, GCF of Fractions for 82/21, 80/51, 20/86 is 2/30702.