Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 538/391,214/616,154/456
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 538,214,154
Greatest Common Factor of Numerators i.e. GCF of 538,214,154 is 2 .
LCM of Denominators means LCM of 391,616,456 as per the given fractions.
LCM of 391,616,456 is 13728792 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 538,214,154
2 | 538, 214, 154 |
269, 107, 77 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 538
List of positive integer factors of 538 that divides 538 without a remainder.
1,2,269,538
Factors of 214
List of positive integer factors of 214 that divides 214 without a remainder.
1,2,107,214
Factors of 154
List of positive integer factors of 154 that divides 154 without a remainder.
1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 538,214,154 . The biggest common factor number is the GCF number.
So the greatest common factor 538,214,154 is 2.
Lets's calculate LCM of 391,616,456
2 | 391, 616, 456 |
2 | 391, 308, 228 |
2 | 391, 154, 114 |
391, 77, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 391 x 77 x 57 = 13728792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/13728792
Therefore, the GCF of Fractions 538/391,214/616,154/456 is 2/13728792
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 391,616,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(391,616,456) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(391,616,456) x common factors =1 x 8 = 8
LCM(391,616,456) = ( 391 × 616 × 456 ) / 8
LCM(391,616,456) = 109830336 / 8
LCM(391,616,456) = 13728792
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 538/391, 214/616, 154/456?
Answer: GCF of Numerators as per given numbers 538/391, 214/616, 154/456 is
GCF of Numerators i.e. for 538,214,154 is 2
LCM of denominators i.e. for 391,616,456 is 13728792.
Thus, GCF of Fractions is 2/13728792.Finally, GCF of Fractions for 538/391, 214/616, 154/456 is 2/13728792.