Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/89,78/78,27/37,31/48
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 14,78,27,31
Greatest Common Factor of Numerators i.e. GCF of 14,78,27,31 is 1 .
LCM of Denominators means LCM of 89,78,37,48 as per the given fractions.
LCM of 89,78,37,48 is 2054832 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 14,78,27,31
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Greatest Common Factor
We found the factors 14,78,27,31 . The biggest common factor number is the GCF number.
So the greatest common factor 14,78,27,31 is 1.
Lets's calculate LCM of 89,78,37,48
2 | 89, 78, 37, 48 |
3 | 89, 39, 37, 24 |
89, 13, 37, 8 |
∴ So the LCM of the given numbers is 2 x 3 x 89 x 13 x 37 x 8 = 2054832
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2054832
Therefore, the GCF of Fractions 14/89,78/78,27/37,31/48 is 1/2054832
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 89,78,37,48 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(89,78,37,48) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(89,78,37,48) x common factors =1 x 6 = 6
LCM(89,78,37,48) = ( 89 × 78 × 37 × 48 ) / 6
LCM(89,78,37,48) = 12328992 / 6
LCM(89,78,37,48) = 2054832
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 14/89, 78/78, 27/37, 31/48?
Answer: GCF of Numerators as per given numbers 14/89, 78/78, 27/37, 31/48 is
GCF of Numerators i.e. for 14,78,27,31 is 1
LCM of denominators i.e. for 89,78,37,48 is 2054832.
Thus, GCF of Fractions is 1/2054832.Finally, GCF of Fractions for 14/89, 78/78, 27/37, 31/48 is 1/2054832.