Use our free GCF of Fractions Calculator tool to compute the GCF of 96/403, 31/715, 200/198 i.e 1/398970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/403, 31/715, 200/198.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 96/403,31/715,200/198
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 96/403,31/715,200/198, numerators are 96,31,200
Denominators are 403,715,198
The GCF of 96,31,200 is 1 .
LCM of 403,715,198 is 398970.
The greatest common factor of 96/403,31/715,200/198 = [GCF of 96,31,200]/[LCM of 403,715,198]= 1/398970
Therefore, the GCF of 96/403,31/715,200/198 is 1/398970.
To find the highest common factor of 96,31,200, we have to find the factors of both numbers and list the highest common factor.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 31 are 1, 31
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The HCF of 96,31,200 is 1.
Lets's calculate GCF of 96,31,200
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 31
:1,31
Now, list down the factors of 200
:1,2,4,5,8,10,20,25,40,50,100,200
Greatest Common Factor
We found the factors 96,31,200 . The biggest common factor number is the GCF number.
So the greatest common factor 96,31,200 is 1.
Lets's calculate LCM of 403,715,198
11 | 403, 715, 198 |
13 | 403, 65, 18 |
31, 5, 18 |
∴ So the LCM of the given numbers is 11 x 13 x 31 x 5 x 18 = 398970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/398970
Therefore, the GCF of Fractions 96/403,31/715,200/198 is 1/398970
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 403,715,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(403,715,198) = 1
common factors(in case of two or more numbers have common factors) = 143
GCF(403,715,198) x common factors =1 x 143 = 143
LCM(403,715,198) = ( 403 × 715 × 198 ) / 143
LCM(403,715,198) = 57052710 / 143
LCM(403,715,198) = 398970
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 96,31,200?
The HCF of 96,31,200 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 96/403, 31/715, 200/198?
Answer: GCF of Numerators as per given numbers 96/403, 31/715, 200/198 is
GCF of Numerators i.e. for 96,31,200 is 1
LCM of denominators i.e. for 403,715,198 is 398970.
Thus, GCF of Fractions is 1/398970.Finally, GCF of Fractions for 96/403, 31/715, 200/198 is 1/398970.