Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 54/71,396/11,324/13
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 54,396,324
Greatest Common Factor of Numerators i.e. GCF of 54,396,324 is 18 .
LCM of Denominators means LCM of 71,11,13 as per the given fractions.
LCM of 71,11,13 is 10153 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 54,396,324
2 | 54, 396, 324 |
3 | 27, 198, 162 |
3 | 9, 66, 54 |
3, 22, 18 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1,2,3,6,9,18,27,54
Factors of 396
List of positive integer factors of 396 that divides 396 without a remainder.
1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Factors of 324
List of positive integer factors of 324 that divides 324 without a remainder.
1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Greatest Common Factor
We found the factors 54,396,324 . The biggest common factor number is the GCF number.
So the greatest common factor 54,396,324 is 18.
Lets's calculate LCM of 71,11,13
Given numbers has no common factors except 1. So, there LCM is their product i.e 10153
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/10153
Therefore, the GCF of Fractions 54/71,396/11,324/13 is 18/10153
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 71,11,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,11,13) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,11,13) x common factors =1 x 1 = 1
LCM(71,11,13) = ( 71 × 11 × 13 ) / 1
LCM(71,11,13) = 10153 / 1
LCM(71,11,13) = 10153
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 54/71, 396/11, 324/13?
Answer: GCF of Numerators as per given numbers 54/71, 396/11, 324/13 is
GCF of Numerators i.e. for 54,396,324 is 18
LCM of denominators i.e. for 71,11,13 is 10153.
Thus, GCF of Fractions is 18/10153.Finally, GCF of Fractions for 54/71, 396/11, 324/13 is 18/10153.