Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8/38,71/31,14/258,867/509
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 8,71,14,867
Greatest Common Factor of Numerators i.e. GCF of 8,71,14,867 is 1 .
LCM of Denominators means LCM of 38,31,258,509 as per the given fractions.
LCM of 38,31,258,509 is 77348658 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 8,71,14,867
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1,2,4,8
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 867
List of positive integer factors of 867 that divides 867 without a remainder.
1,3,17,51,289,867
Greatest Common Factor
We found the factors 8,71,14,867 . The biggest common factor number is the GCF number.
So the greatest common factor 8,71,14,867 is 1.
Lets's calculate LCM of 38,31,258,509
2 | 38, 31, 258, 509 |
19, 31, 129, 509 |
∴ So the LCM of the given numbers is 2 x 19 x 31 x 129 x 509 = 77348658
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77348658
Therefore, the GCF of Fractions 8/38,71/31,14/258,867/509 is 1/77348658
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 38,31,258,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,31,258,509) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(38,31,258,509) x common factors =1 x 2 = 2
LCM(38,31,258,509) = ( 38 × 31 × 258 × 509 ) / 2
LCM(38,31,258,509) = 154697316 / 2
LCM(38,31,258,509) = 77348658
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 8/38, 71/31, 14/258, 867/509?
Answer: GCF of Numerators as per given numbers 8/38, 71/31, 14/258, 867/509 is
GCF of Numerators i.e. for 8,71,14,867 is 1
LCM of denominators i.e. for 38,31,258,509 is 77348658.
Thus, GCF of Fractions is 1/77348658.Finally, GCF of Fractions for 8/38, 71/31, 14/258, 867/509 is 1/77348658.