Use our free GCF of Fractions Calculator tool to compute the GCF of 71/174, 82/8439 i.e 1/16878 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/174, 82/8439.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 71/174,82/8439
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 71/174,82/8439, numerators are 71,82
Denominators are 174,8439
The GCF of 71,82 is 1 .
LCM of 174,8439 is 16878.
The greatest common factor of 71/174,82/8439 = [GCF of 71,82]/[LCM of 174,8439]= 1/16878
Therefore, the GCF of 71/174,82/8439 is 1/16878.
To find the highest common factor of 71,82, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 82 are 1, 2, 41, 82
The HCF of 71,82 is 1.
Lets's calculate GCF of 71,82
∴ So GCF of numbers is 1 because of no common factors present between them.
Lets's calculate LCM of 174,8439
3 | 174, 8439 |
29 | 58, 2813 |
2, 97 |
∴ So the LCM of the given numbers is 3 x 29 x 2 x 97 = 16878
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16878
Therefore, the GCF of Fractions 71/174,82/8439 is 1/16878
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 174,8439 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,8439) = 87
common factors(in case of two or more numbers have common factors) = 1
GCF(174,8439) x common factors =87 x 1 = 87
LCM(174,8439) = ( 174 × 8439 ) / 87
LCM(174,8439) = 1468386 / 87
LCM(174,8439) = 16878
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 71,82?
The HCF of 71,82 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 71/174, 82/8439?
Answer: GCF of Numerators as per given numbers 71/174, 82/8439 is
GCF of Numerators i.e. for 71,82 is 1
LCM of denominators i.e. for 174,8439 is 16878.
Thus, GCF of Fractions is 1/16878.Finally, GCF of Fractions for 71/174, 82/8439 is 1/16878.