Use our free GCF of Fractions Calculator tool to compute the GCF of 520/75, 816/517 i.e 8/38775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/75, 816/517.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 520/75,816/517
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 520/75,816/517, numerators are 520,816
Denominators are 75,517
The GCF of 520,816 is 8 .
LCM of 75,517 is 38775.
The greatest common factor of 520/75,816/517 = [GCF of 520,816]/[LCM of 75,517]= 8/38775
Therefore, the GCF of 520/75,816/517 is 8/38775.
To find the highest common factor of 520,816, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
The HCF of 520,816 is 8.
Lets's calculate GCF of 520,816
2 | 520, 816 |
2 | 260, 408 |
2 | 130, 204 |
65, 102 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Now, list down the factors of 816
:1,2,3,4,6,8,12,16,17,24,34,48,51,68,102,136,204,272,408,816
Greatest Common Factor
We found the factors 520,816 . The biggest common factor number is the GCF number.
So the greatest common factor 520,816 is 8.
Lets's calculate LCM of 75,517
Given numbers has no common factors except 1. So, there LCM is their product i.e 38775
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/38775
Therefore, the GCF of Fractions 520/75,816/517 is 8/38775
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 75,517 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,517) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,517) x common factors =1 x 1 = 1
LCM(75,517) = ( 75 × 517 ) / 1
LCM(75,517) = 38775 / 1
LCM(75,517) = 38775
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 520,816?
The HCF of 520,816 is 8
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 520/75, 816/517?
Answer: GCF of Numerators as per given numbers 520/75, 816/517 is
GCF of Numerators i.e. for 520,816 is 8
LCM of denominators i.e. for 75,517 is 38775.
Thus, GCF of Fractions is 8/38775.Finally, GCF of Fractions for 520/75, 816/517 is 8/38775.