Use our free GCF of Fractions Calculator tool to compute the GCF of 728/323, 819/415 i.e 91/134045 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/323, 819/415.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 728/323,819/415
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 728/323,819/415, numerators are 728,819
Denominators are 323,415
The GCF of 728,819 is 91 .
LCM of 323,415 is 134045.
The greatest common factor of 728/323,819/415 = [GCF of 728,819]/[LCM of 323,415]= 91/134045
Therefore, the GCF of 728/323,819/415 is 91/134045.
To find the highest common factor of 728,819, 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 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The HCF of 728,819 is 91.
Lets's calculate GCF of 728,819
7 | 728, 819 |
13 | 104, 117 |
8, 9 |
∴ So the GCF of the given numbers is 7 x 13 = 91
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 819
:1,3,7,9,13,21,39,63,91,117,273,819
Greatest Common Factor
We found the factors 728,819 . The biggest common factor number is the GCF number.
So the greatest common factor 728,819 is 91.
Lets's calculate LCM of 323,415
Given numbers has no common factors except 1. So, there LCM is their product i.e 134045
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 91/134045
Therefore, the GCF of Fractions 728/323,819/415 is 91/134045
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 323,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(323,415) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(323,415) x common factors =1 x 1 = 1
LCM(323,415) = ( 323 × 415 ) / 1
LCM(323,415) = 134045 / 1
LCM(323,415) = 134045
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 728,819?
The HCF of 728,819 is 91
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 728/323, 819/415?
Answer: GCF of Numerators as per given numbers 728/323, 819/415 is
GCF of Numerators i.e. for 728,819 is 91
LCM of denominators i.e. for 323,415 is 134045.
Thus, GCF of Fractions is 91/134045.Finally, GCF of Fractions for 728/323, 819/415 is 91/134045.