Use our free GCF of Fractions Calculator tool to compute the GCF of 728/741, 665/738 i.e 7/182286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/741, 665/738.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 728/741,665/738
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 728/741,665/738, numerators are 728,665
Denominators are 741,738
The GCF of 728,665 is 7 .
LCM of 741,738 is 182286.
The greatest common factor of 728/741,665/738 = [GCF of 728,665]/[LCM of 741,738]= 7/182286
Therefore, the GCF of 728/741,665/738 is 7/182286.
To find the highest common factor of 728,665, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The HCF of 728,665 is 7.
Lets's calculate GCF of 728,665
7 | 728, 665 |
104, 95 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Greatest Common Factor
We found the factors 728,665 . The biggest common factor number is the GCF number.
So the greatest common factor 728,665 is 7.
Lets's calculate LCM of 741,738
3 | 741, 738 |
247, 246 |
∴ So the LCM of the given numbers is 3 x 247 x 246 = 182286
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/182286
Therefore, the GCF of Fractions 728/741,665/738 is 7/182286
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 741,738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(741,738) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(741,738) x common factors =3 x 1 = 3
LCM(741,738) = ( 741 × 738 ) / 3
LCM(741,738) = 546858 / 3
LCM(741,738) = 182286
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 728,665?
The HCF of 728,665 is 7
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 728/741, 665/738?
Answer: GCF of Numerators as per given numbers 728/741, 665/738 is
GCF of Numerators i.e. for 728,665 is 7
LCM of denominators i.e. for 741,738 is 182286.
Thus, GCF of Fractions is 7/182286.Finally, GCF of Fractions for 728/741, 665/738 is 7/182286.