Use our free GCF of Fractions Calculator tool to compute the GCF of 521/309, 510/759 i.e 1/78177 easily. The following is the detailed procedure to determine the greatest common factor of fractions 521/309, 510/759.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 521/309,510/759
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 521/309,510/759, numerators are 521,510
Denominators are 309,759
The GCF of 521,510 is 1 .
LCM of 309,759 is 78177.
The greatest common factor of 521/309,510/759 = [GCF of 521,510]/[LCM of 309,759]= 1/78177
Therefore, the GCF of 521/309,510/759 is 1/78177.
To find the highest common factor of 521,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 521 are 1, 521
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 521,510 is 1.
Lets's calculate GCF of 521,510
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 521
:1,521
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 521,510 . The biggest common factor number is the GCF number.
So the greatest common factor 521,510 is 1.
Lets's calculate LCM of 309,759
3 | 309, 759 |
103, 253 |
∴ So the LCM of the given numbers is 3 x 103 x 253 = 78177
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/78177
Therefore, the GCF of Fractions 521/309,510/759 is 1/78177
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 309,759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,759) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,759) x common factors =3 x 1 = 3
LCM(309,759) = ( 309 × 759 ) / 3
LCM(309,759) = 234531 / 3
LCM(309,759) = 78177
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 521,510?
The HCF of 521,510 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 521/309, 510/759?
Answer: GCF of Numerators as per given numbers 521/309, 510/759 is
GCF of Numerators i.e. for 521,510 is 1
LCM of denominators i.e. for 309,759 is 78177.
Thus, GCF of Fractions is 1/78177.Finally, GCF of Fractions for 521/309, 510/759 is 1/78177.