Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 205/311,7435/231
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 205,7435
Greatest Common Factor of Numerators i.e. GCF of 205,7435 is 5 .
LCM of Denominators means LCM of 311,231 as per the given fractions.
LCM of 311,231 is 71841 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 205,7435
5 | 205, 7435 |
41, 1487 |
∴ So the GCF of the given numbers is 5 = 5
Factors of 205
List of positive integer factors of 205 that divides 205 without a remainder.
1,5,41,205
Factors of 7435
List of positive integer factors of 7435 that divides 7435 without a remainder.
1,5,1487,7435
Greatest Common Factor
We found the factors 205,7435 . The biggest common factor number is the GCF number.
So the greatest common factor 205,7435 is 5.
Lets's calculate LCM of 311,231
Given numbers has no common factors except 1. So, there LCM is their product i.e 71841
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/71841
Therefore, the GCF of Fractions 205/311,7435/231 is 5/71841
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 311,231 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(311,231) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(311,231) x common factors =1 x 1 = 1
LCM(311,231) = ( 311 × 231 ) / 1
LCM(311,231) = 71841 / 1
LCM(311,231) = 71841
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 205/311, 7435/231?
Answer: GCF of Numerators as per given numbers 205/311, 7435/231 is
GCF of Numerators i.e. for 205,7435 is 5
LCM of denominators i.e. for 311,231 is 71841.
Thus, GCF of Fractions is 5/71841.Finally, GCF of Fractions for 205/311, 7435/231 is 5/71841.