Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 9/52,31/54,46/309,422/711
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 9,31,46,422
Greatest Common Factor of Numerators i.e. GCF of 9,31,46,422 is 1 .
LCM of Denominators means LCM of 52,54,309,711 as per the given fractions.
LCM of 52,54,309,711 is 11424348 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 9,31,46,422
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 9
List of positive integer factors of 9 that divides 9 without a remainder.
1,3,9
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1,2,23,46
Factors of 422
List of positive integer factors of 422 that divides 422 without a remainder.
1,2,211,422
Greatest Common Factor
We found the factors 9,31,46,422 . The biggest common factor number is the GCF number.
So the greatest common factor 9,31,46,422 is 1.
Lets's calculate LCM of 52,54,309,711
2 | 52, 54, 309, 711 |
3 | 26, 27, 309, 711 |
3 | 26, 9, 103, 237 |
26, 3, 103, 79 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 26 x 3 x 103 x 79 = 11424348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11424348
Therefore, the GCF of Fractions 9/52,31/54,46/309,422/711 is 1/11424348
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 52,54,309,711 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,54,309,711) = 1
common factors(in case of two or more numbers have common factors) = 54
GCF(52,54,309,711) x common factors =1 x 54 = 54
LCM(52,54,309,711) = ( 52 × 54 × 309 × 711 ) / 54
LCM(52,54,309,711) = 616914792 / 54
LCM(52,54,309,711) = 11424348
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 9/52, 31/54, 46/309, 422/711?
Answer: GCF of Numerators as per given numbers 9/52, 31/54, 46/309, 422/711 is
GCF of Numerators i.e. for 9,31,46,422 is 1
LCM of denominators i.e. for 52,54,309,711 is 11424348.
Thus, GCF of Fractions is 1/11424348.Finally, GCF of Fractions for 9/52, 31/54, 46/309, 422/711 is 1/11424348.