Use our free GCF of Fractions Calculator tool to compute the GCF of 7967/195, 7657/455 i.e 31/1365 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7967/195, 7657/455.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7967/195,7657/455
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 7967/195,7657/455, numerators are 7967,7657
Denominators are 195,455
The GCF of 7967,7657 is 31 .
LCM of 195,455 is 1365.
The greatest common factor of 7967/195,7657/455 = [GCF of 7967,7657]/[LCM of 195,455]= 31/1365
Therefore, the GCF of 7967/195,7657/455 is 31/1365.
To find the highest common factor of 7967,7657, we have to find the factors of both numbers and list the highest common factor.
The factors of 7967 are 1, 31, 257, 7967
The factors of 7657 are 1, 13, 19, 31, 247, 403, 589, 7657
The HCF of 7967,7657 is 31.
Lets's calculate GCF of 7967,7657
31 | 7967, 7657 |
257, 247 |
∴ So the GCF of the given numbers is 31 = 31
Now, list down the factors of 7967
:1,31,257,7967
Now, list down the factors of 7657
:1,13,19,31,247,403,589,7657
Greatest Common Factor
We found the factors 7967,7657 . The biggest common factor number is the GCF number.
So the greatest common factor 7967,7657 is 31.
Lets's calculate LCM of 195,455
5 | 195, 455 |
13 | 39, 91 |
3, 7 |
∴ So the LCM of the given numbers is 5 x 13 x 3 x 7 = 1365
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/1365
Therefore, the GCF of Fractions 7967/195,7657/455 is 31/1365
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 195,455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(195,455) = 65
common factors(in case of two or more numbers have common factors) = 1
GCF(195,455) x common factors =65 x 1 = 65
LCM(195,455) = ( 195 × 455 ) / 65
LCM(195,455) = 88725 / 65
LCM(195,455) = 1365
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7967,7657?
The HCF of 7967,7657 is 31
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 7967/195, 7657/455?
Answer: GCF of Numerators as per given numbers 7967/195, 7657/455 is
GCF of Numerators i.e. for 7967,7657 is 31
LCM of denominators i.e. for 195,455 is 1365.
Thus, GCF of Fractions is 31/1365.Finally, GCF of Fractions for 7967/195, 7657/455 is 31/1365.