Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 218/51,407/51,714/942
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 218,407,714
Greatest Common Factor of Numerators i.e. GCF of 218,407,714 is 1 .
LCM of Denominators means LCM of 51,51,942 as per the given fractions.
LCM of 51,51,942 is 16014 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 218,407,714
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 218
List of positive integer factors of 218 that divides 218 without a remainder.
1,2,109,218
Factors of 407
List of positive integer factors of 407 that divides 407 without a remainder.
1,11,37,407
Factors of 714
List of positive integer factors of 714 that divides 714 without a remainder.
1,2,3,6,7,14,17,21,34,42,51,102,119,238,357,714
Greatest Common Factor
We found the factors 218,407,714 . The biggest common factor number is the GCF number.
So the greatest common factor 218,407,714 is 1.
Lets's calculate LCM of 51,51,942
3 | 51, 51, 942 |
17 | 17, 17, 314 |
1, 1, 314 |
∴ So the LCM of the given numbers is 3 x 17 x 1 x 1 x 314 = 16014
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16014
Therefore, the GCF of Fractions 218/51,407/51,714/942 is 1/16014
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 51,51,942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,51,942) = 3
common factors(in case of two or more numbers have common factors) = 51
GCF(51,51,942) x common factors =3 x 51 = 153
LCM(51,51,942) = ( 51 × 51 × 942 ) / 153
LCM(51,51,942) = 2450142 / 153
LCM(51,51,942) = 16014
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 218/51, 407/51, 714/942?
Answer: GCF of Numerators as per given numbers 218/51, 407/51, 714/942 is
GCF of Numerators i.e. for 218,407,714 is 1
LCM of denominators i.e. for 51,51,942 is 16014.
Thus, GCF of Fractions is 1/16014.Finally, GCF of Fractions for 218/51, 407/51, 714/942 is 1/16014.