Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/58,60/39,998/81
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 42,60,998
Greatest Common Factor of Numerators i.e. GCF of 42,60,998 is 2 .
LCM of Denominators means LCM of 58,39,81 as per the given fractions.
LCM of 58,39,81 is 61074 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 42,60,998
2 | 42, 60, 998 |
21, 30, 499 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1,2,3,4,5,6,10,12,15,20,30,60
Factors of 998
List of positive integer factors of 998 that divides 998 without a remainder.
1,2,499,998
Greatest Common Factor
We found the factors 42,60,998 . The biggest common factor number is the GCF number.
So the greatest common factor 42,60,998 is 2.
Lets's calculate LCM of 58,39,81
3 | 58, 39, 81 |
58, 13, 27 |
∴ So the LCM of the given numbers is 3 x 58 x 13 x 27 = 61074
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/61074
Therefore, the GCF of Fractions 42/58,60/39,998/81 is 2/61074
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 58,39,81 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,39,81) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(58,39,81) x common factors =1 x 3 = 3
LCM(58,39,81) = ( 58 × 39 × 81 ) / 3
LCM(58,39,81) = 183222 / 3
LCM(58,39,81) = 61074
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 42/58, 60/39, 998/81?
Answer: GCF of Numerators as per given numbers 42/58, 60/39, 998/81 is
GCF of Numerators i.e. for 42,60,998 is 2
LCM of denominators i.e. for 58,39,81 is 61074.
Thus, GCF of Fractions is 2/61074.Finally, GCF of Fractions for 42/58, 60/39, 998/81 is 2/61074.