Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/71,63/57,82/57,586/20
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 78,63,82,586
Greatest Common Factor of Numerators i.e. GCF of 78,63,82,586 is 1 .
LCM of Denominators means LCM of 71,57,57,20 as per the given fractions.
LCM of 71,57,57,20 is 80940 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 78,63,82,586
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1,3,7,9,21,63
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Factors of 586
List of positive integer factors of 586 that divides 586 without a remainder.
1,2,293,586
Greatest Common Factor
We found the factors 78,63,82,586 . The biggest common factor number is the GCF number.
So the greatest common factor 78,63,82,586 is 1.
Lets's calculate LCM of 71,57,57,20
3 | 71, 57, 57, 20 |
19 | 71, 19, 19, 20 |
71, 1, 1, 20 |
∴ So the LCM of the given numbers is 3 x 19 x 71 x 1 x 1 x 20 = 80940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/80940
Therefore, the GCF of Fractions 78/71,63/57,82/57,586/20 is 1/80940
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 71,57,57,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,57,57,20) = 1
common factors(in case of two or more numbers have common factors) = 57
GCF(71,57,57,20) x common factors =1 x 57 = 57
LCM(71,57,57,20) = ( 71 × 57 × 57 × 20 ) / 57
LCM(71,57,57,20) = 4613580 / 57
LCM(71,57,57,20) = 80940
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 78/71, 63/57, 82/57, 586/20?
Answer: GCF of Numerators as per given numbers 78/71, 63/57, 82/57, 586/20 is
GCF of Numerators i.e. for 78,63,82,586 is 1
LCM of denominators i.e. for 71,57,57,20 is 80940.
Thus, GCF of Fractions is 1/80940.Finally, GCF of Fractions for 78/71, 63/57, 82/57, 586/20 is 1/80940.