Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 34/59,92/81,60/16,218/51
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 34,92,60,218
Greatest Common Factor of Numerators i.e. GCF of 34,92,60,218 is 2 .
LCM of Denominators means LCM of 59,81,16,51 as per the given fractions.
LCM of 59,81,16,51 is 1299888 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 34,92,60,218
2 | 34, 92, 60, 218 |
17, 46, 30, 109 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 92
List of positive integer factors of 92 that divides 92 without a remainder.
1,2,4,23,46,92
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 218
List of positive integer factors of 218 that divides 218 without a remainder.
1,2,109,218
Greatest Common Factor
We found the factors 34,92,60,218 . The biggest common factor number is the GCF number.
So the greatest common factor 34,92,60,218 is 2.
Lets's calculate LCM of 59,81,16,51
3 | 59, 81, 16, 51 |
59, 27, 16, 17 |
∴ So the LCM of the given numbers is 3 x 59 x 27 x 16 x 17 = 1299888
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1299888
Therefore, the GCF of Fractions 34/59,92/81,60/16,218/51 is 2/1299888
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 59,81,16,51 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(59,81,16,51) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(59,81,16,51) x common factors =1 x 3 = 3
LCM(59,81,16,51) = ( 59 × 81 × 16 × 51 ) / 3
LCM(59,81,16,51) = 3899664 / 3
LCM(59,81,16,51) = 1299888
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 34/59, 92/81, 60/16, 218/51?
Answer: GCF of Numerators as per given numbers 34/59, 92/81, 60/16, 218/51 is
GCF of Numerators i.e. for 34,92,60,218 is 2
LCM of denominators i.e. for 59,81,16,51 is 1299888.
Thus, GCF of Fractions is 2/1299888.Finally, GCF of Fractions for 34/59, 92/81, 60/16, 218/51 is 2/1299888.