Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 12/35,32/50,27/19,115/31
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 12,32,27,115
Greatest Common Factor of Numerators i.e. GCF of 12,32,27,115 is 1 .
LCM of Denominators means LCM of 35,50,19,31 as per the given fractions.
LCM of 35,50,19,31 is 206150 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 12,32,27,115
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1,2,4,8,16,32
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 115
List of positive integer factors of 115 that divides 115 without a remainder.
1,5,23,115
Greatest Common Factor
We found the factors 12,32,27,115 . The biggest common factor number is the GCF number.
So the greatest common factor 12,32,27,115 is 1.
Lets's calculate LCM of 35,50,19,31
5 | 35, 50, 19, 31 |
7, 10, 19, 31 |
∴ So the LCM of the given numbers is 5 x 7 x 10 x 19 x 31 = 206150
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/206150
Therefore, the GCF of Fractions 12/35,32/50,27/19,115/31 is 1/206150
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 35,50,19,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,50,19,31) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(35,50,19,31) x common factors =1 x 5 = 5
LCM(35,50,19,31) = ( 35 × 50 × 19 × 31 ) / 5
LCM(35,50,19,31) = 1030750 / 5
LCM(35,50,19,31) = 206150
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 12/35, 32/50, 27/19, 115/31?
Answer: GCF of Numerators as per given numbers 12/35, 32/50, 27/19, 115/31 is
GCF of Numerators i.e. for 12,32,27,115 is 1
LCM of denominators i.e. for 35,50,19,31 is 206150.
Thus, GCF of Fractions is 1/206150.Finally, GCF of Fractions for 12/35, 32/50, 27/19, 115/31 is 1/206150.