Use our free GCF of Fractions Calculator tool to compute the GCF of 517/582, 710/123 i.e 1/23862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 517/582, 710/123.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 517/582,710/123
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 517/582,710/123, numerators are 517,710
Denominators are 582,123
The GCF of 517,710 is 1 .
LCM of 582,123 is 23862.
The greatest common factor of 517/582,710/123 = [GCF of 517,710]/[LCM of 582,123]= 1/23862
Therefore, the GCF of 517/582,710/123 is 1/23862.
To find the highest common factor of 517,710, we have to find the factors of both numbers and list the highest common factor.
The factors of 517 are 1, 11, 47, 517
The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710
The HCF of 517,710 is 1.
Lets's calculate GCF of 517,710
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 517
:1,11,47,517
Now, list down the factors of 710
:1,2,5,10,71,142,355,710
Greatest Common Factor
We found the factors 517,710 . The biggest common factor number is the GCF number.
So the greatest common factor 517,710 is 1.
Lets's calculate LCM of 582,123
3 | 582, 123 |
194, 41 |
∴ So the LCM of the given numbers is 3 x 194 x 41 = 23862
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23862
Therefore, the GCF of Fractions 517/582,710/123 is 1/23862
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 582,123 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(582,123) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(582,123) x common factors =3 x 1 = 3
LCM(582,123) = ( 582 × 123 ) / 3
LCM(582,123) = 71586 / 3
LCM(582,123) = 23862
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 517,710?
The HCF of 517,710 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 517/582, 710/123?
Answer: GCF of Numerators as per given numbers 517/582, 710/123 is
GCF of Numerators i.e. for 517,710 is 1
LCM of denominators i.e. for 582,123 is 23862.
Thus, GCF of Fractions is 1/23862.Finally, GCF of Fractions for 517/582, 710/123 is 1/23862.