Use our free GCF of Fractions Calculator tool to compute the GCF of 540/156, 198/976 i.e 18/38064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/156, 198/976.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 540/156,198/976
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 540/156,198/976, numerators are 540,198
Denominators are 156,976
The GCF of 540,198 is 18 .
LCM of 156,976 is 38064.
The greatest common factor of 540/156,198/976 = [GCF of 540,198]/[LCM of 156,976]= 18/38064
Therefore, the GCF of 540/156,198/976 is 18/38064.
To find the highest common factor of 540,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 540,198 is 18.
Lets's calculate GCF of 540,198
2 | 540, 198 |
3 | 270, 99 |
3 | 90, 33 |
30, 11 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 540,198 . The biggest common factor number is the GCF number.
So the greatest common factor 540,198 is 18.
Lets's calculate LCM of 156,976
2 | 156, 976 |
2 | 78, 488 |
39, 244 |
∴ So the LCM of the given numbers is 2 x 2 x 39 x 244 = 38064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/38064
Therefore, the GCF of Fractions 540/156,198/976 is 18/38064
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 156,976 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(156,976) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(156,976) x common factors =4 x 1 = 4
LCM(156,976) = ( 156 × 976 ) / 4
LCM(156,976) = 152256 / 4
LCM(156,976) = 38064
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 540,198?
The HCF of 540,198 is 18
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 540/156, 198/976?
Answer: GCF of Numerators as per given numbers 540/156, 198/976 is
GCF of Numerators i.e. for 540,198 is 18
LCM of denominators i.e. for 156,976 is 38064.
Thus, GCF of Fractions is 18/38064.Finally, GCF of Fractions for 540/156, 198/976 is 18/38064.