Use our free GCF of Fractions Calculator tool to compute the GCF of 981/78, 654/188 i.e 327/7332 easily. The following is the detailed procedure to determine the greatest common factor of fractions 981/78, 654/188.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 981/78,654/188
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 981/78,654/188, numerators are 981,654
Denominators are 78,188
The GCF of 981,654 is 327 .
LCM of 78,188 is 7332.
The greatest common factor of 981/78,654/188 = [GCF of 981,654]/[LCM of 78,188]= 327/7332
Therefore, the GCF of 981/78,654/188 is 327/7332.
To find the highest common factor of 981,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 981 are 1, 3, 9, 109, 327, 981
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 981,654 is 327.
Lets's calculate GCF of 981,654
3 | 981, 654 |
109 | 327, 218 |
3, 2 |
∴ So the GCF of the given numbers is 3 x 109 = 327
Now, list down the factors of 981
:1,3,9,109,327,981
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 981,654 . The biggest common factor number is the GCF number.
So the greatest common factor 981,654 is 327.
Lets's calculate LCM of 78,188
2 | 78, 188 |
39, 94 |
∴ So the LCM of the given numbers is 2 x 39 x 94 = 7332
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 327/7332
Therefore, the GCF of Fractions 981/78,654/188 is 327/7332
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 78,188 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,188) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(78,188) x common factors =2 x 1 = 2
LCM(78,188) = ( 78 × 188 ) / 2
LCM(78,188) = 14664 / 2
LCM(78,188) = 7332
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 981,654?
The HCF of 981,654 is 327
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 981/78, 654/188?
Answer: GCF of Numerators as per given numbers 981/78, 654/188 is
GCF of Numerators i.e. for 981,654 is 327
LCM of denominators i.e. for 78,188 is 7332.
Thus, GCF of Fractions is 327/7332.Finally, GCF of Fractions for 981/78, 654/188 is 327/7332.