Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 39/65,54/73,57/40
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 39,54,57
Greatest Common Factor of Numerators i.e. GCF of 39,54,57 is 3 .
LCM of Denominators means LCM of 65,73,40 as per the given fractions.
LCM of 65,73,40 is 37960 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 39,54,57
3 | 39, 54, 57 |
13, 18, 19 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1,3,13,39
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 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Greatest Common Factor
We found the factors 39,54,57 . The biggest common factor number is the GCF number.
So the greatest common factor 39,54,57 is 3.
Lets's calculate LCM of 65,73,40
5 | 65, 73, 40 |
13, 73, 8 |
∴ So the LCM of the given numbers is 5 x 13 x 73 x 8 = 37960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/37960
Therefore, the GCF of Fractions 39/65,54/73,57/40 is 3/37960
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 65,73,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,73,40) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(65,73,40) x common factors =1 x 5 = 5
LCM(65,73,40) = ( 65 × 73 × 40 ) / 5
LCM(65,73,40) = 189800 / 5
LCM(65,73,40) = 37960
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 39/65, 54/73, 57/40?
Answer: GCF of Numerators as per given numbers 39/65, 54/73, 57/40 is
GCF of Numerators i.e. for 39,54,57 is 3
LCM of denominators i.e. for 65,73,40 is 37960.
Thus, GCF of Fractions is 3/37960.Finally, GCF of Fractions for 39/65, 54/73, 57/40 is 3/37960.