Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3/37,90/42,76/189,768/313
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 3,90,76,768
Greatest Common Factor of Numerators i.e. GCF of 3,90,76,768 is 1 .
LCM of Denominators means LCM of 37,42,189,313 as per the given fractions.
LCM of 37,42,189,313 is 4377618 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 3,90,76,768
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1,3
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 768
List of positive integer factors of 768 that divides 768 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 3,90,76,768 . The biggest common factor number is the GCF number.
So the greatest common factor 3,90,76,768 is 1.
Lets's calculate LCM of 37,42,189,313
3 | 37, 42, 189, 313 |
7 | 37, 14, 63, 313 |
37, 2, 9, 313 |
∴ So the LCM of the given numbers is 3 x 7 x 37 x 2 x 9 x 313 = 4377618
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4377618
Therefore, the GCF of Fractions 3/37,90/42,76/189,768/313 is 1/4377618
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 37,42,189,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(37,42,189,313) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(37,42,189,313) x common factors =1 x 21 = 21
LCM(37,42,189,313) = ( 37 × 42 × 189 × 313 ) / 21
LCM(37,42,189,313) = 91929978 / 21
LCM(37,42,189,313) = 4377618
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 3/37, 90/42, 76/189, 768/313?
Answer: GCF of Numerators as per given numbers 3/37, 90/42, 76/189, 768/313 is
GCF of Numerators i.e. for 3,90,76,768 is 1
LCM of denominators i.e. for 37,42,189,313 is 4377618.
Thus, GCF of Fractions is 1/4377618.Finally, GCF of Fractions for 3/37, 90/42, 76/189, 768/313 is 1/4377618.