Use our free GCF of Fractions Calculator tool to compute the GCF of 513/689, 663/382 i.e 3/263198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/689, 663/382.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 513/689,663/382
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 513/689,663/382, numerators are 513,663
Denominators are 689,382
The GCF of 513,663 is 3 .
LCM of 689,382 is 263198.
The greatest common factor of 513/689,663/382 = [GCF of 513,663]/[LCM of 689,382]= 3/263198
Therefore, the GCF of 513/689,663/382 is 3/263198.
To find the highest common factor of 513,663, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The HCF of 513,663 is 3.
Lets's calculate GCF of 513,663
3 | 513, 663 |
171, 221 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
Greatest Common Factor
We found the factors 513,663 . The biggest common factor number is the GCF number.
So the greatest common factor 513,663 is 3.
Lets's calculate LCM of 689,382
Given numbers has no common factors except 1. So, there LCM is their product i.e 263198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/263198
Therefore, the GCF of Fractions 513/689,663/382 is 3/263198
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 689,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,382) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,382) x common factors =1 x 1 = 1
LCM(689,382) = ( 689 × 382 ) / 1
LCM(689,382) = 263198 / 1
LCM(689,382) = 263198
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 513,663?
The HCF of 513,663 is 3
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 513/689, 663/382?
Answer: GCF of Numerators as per given numbers 513/689, 663/382 is
GCF of Numerators i.e. for 513,663 is 3
LCM of denominators i.e. for 689,382 is 263198.
Thus, GCF of Fractions is 3/263198.Finally, GCF of Fractions for 513/689, 663/382 is 3/263198.