Use our free GCF of Fractions Calculator tool to compute the GCF of 195/816, 988/459 i.e 13/7344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 195/816, 988/459.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 195/816,988/459
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 195/816,988/459, numerators are 195,988
Denominators are 816,459
The GCF of 195,988 is 13 .
LCM of 816,459 is 7344.
The greatest common factor of 195/816,988/459 = [GCF of 195,988]/[LCM of 816,459]= 13/7344
Therefore, the GCF of 195/816,988/459 is 13/7344.
To find the highest common factor of 195,988, we have to find the factors of both numbers and list the highest common factor.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195
The factors of 988 are 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988
The HCF of 195,988 is 13.
Lets's calculate GCF of 195,988
13 | 195, 988 |
15, 76 |
∴ So the GCF of the given numbers is 13 = 13
Now, list down the factors of 195
:1,3,5,13,15,39,65,195
Now, list down the factors of 988
:1,2,4,13,19,26,38,52,76,247,494,988
Greatest Common Factor
We found the factors 195,988 . The biggest common factor number is the GCF number.
So the greatest common factor 195,988 is 13.
Lets's calculate LCM of 816,459
3 | 816, 459 |
17 | 272, 153 |
16, 9 |
∴ So the LCM of the given numbers is 3 x 17 x 16 x 9 = 7344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/7344
Therefore, the GCF of Fractions 195/816,988/459 is 13/7344
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 816,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(816,459) = 51
common factors(in case of two or more numbers have common factors) = 1
GCF(816,459) x common factors =51 x 1 = 51
LCM(816,459) = ( 816 × 459 ) / 51
LCM(816,459) = 374544 / 51
LCM(816,459) = 7344
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 195,988?
The HCF of 195,988 is 13
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 195/816, 988/459?
Answer: GCF of Numerators as per given numbers 195/816, 988/459 is
GCF of Numerators i.e. for 195,988 is 13
LCM of denominators i.e. for 816,459 is 7344.
Thus, GCF of Fractions is 13/7344.Finally, GCF of Fractions for 195/816, 988/459 is 13/7344.