Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 31/82,41/17,75/48,66/56
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 31,41,75,66
Greatest Common Factor of Numerators i.e. GCF of 31,41,75,66 is 1 .
LCM of Denominators means LCM of 82,17,48,56 as per the given fractions.
LCM of 82,17,48,56 is 234192 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 31,41,75,66
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Greatest Common Factor
We found the factors 31,41,75,66 . The biggest common factor number is the GCF number.
So the greatest common factor 31,41,75,66 is 1.
Lets's calculate LCM of 82,17,48,56
2 | 82, 17, 48, 56 |
2 | 41, 17, 24, 28 |
2 | 41, 17, 12, 14 |
41, 17, 6, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 41 x 17 x 6 x 7 = 234192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/234192
Therefore, the GCF of Fractions 31/82,41/17,75/48,66/56 is 1/234192
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 82,17,48,56 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,17,48,56) = 1
common factors(in case of two or more numbers have common factors) = 16
GCF(82,17,48,56) x common factors =1 x 16 = 16
LCM(82,17,48,56) = ( 82 × 17 × 48 × 56 ) / 16
LCM(82,17,48,56) = 3747072 / 16
LCM(82,17,48,56) = 234192
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 31/82, 41/17, 75/48, 66/56?
Answer: GCF of Numerators as per given numbers 31/82, 41/17, 75/48, 66/56 is
GCF of Numerators i.e. for 31,41,75,66 is 1
LCM of denominators i.e. for 82,17,48,56 is 234192.
Thus, GCF of Fractions is 1/234192.Finally, GCF of Fractions for 31/82, 41/17, 75/48, 66/56 is 1/234192.