Use our free GCF of Fractions Calculator tool to compute the GCF of 663/691, 510/431 i.e 51/297821 easily. The following is the detailed procedure to determine the greatest common factor of fractions 663/691, 510/431.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 663/691,510/431
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 663/691,510/431, numerators are 663,510
Denominators are 691,431
The GCF of 663,510 is 51 .
LCM of 691,431 is 297821.
The greatest common factor of 663/691,510/431 = [GCF of 663,510]/[LCM of 691,431]= 51/297821
Therefore, the GCF of 663/691,510/431 is 51/297821.
To find the highest common factor of 663,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 663,510 is 51.
Lets's calculate GCF of 663,510
3 | 663, 510 |
17 | 221, 170 |
13, 10 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
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 663,510 . The biggest common factor number is the GCF number.
So the greatest common factor 663,510 is 51.
Lets's calculate LCM of 691,431
Given numbers has no common factors except 1. So, there LCM is their product i.e 297821
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/297821
Therefore, the GCF of Fractions 663/691,510/431 is 51/297821
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 691,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(691,431) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(691,431) x common factors =1 x 1 = 1
LCM(691,431) = ( 691 × 431 ) / 1
LCM(691,431) = 297821 / 1
LCM(691,431) = 297821
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 663,510?
The HCF of 663,510 is 51
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 663/691, 510/431?
Answer: GCF of Numerators as per given numbers 663/691, 510/431 is
GCF of Numerators i.e. for 663,510 is 51
LCM of denominators i.e. for 691,431 is 297821.
Thus, GCF of Fractions is 51/297821.Finally, GCF of Fractions for 663/691, 510/431 is 51/297821.