Use our free GCF of Fractions Calculator tool to compute the GCF of 966/586, 728/395 i.e 14/231470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 966/586, 728/395.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 966/586,728/395
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 966/586,728/395, numerators are 966,728
Denominators are 586,395
The GCF of 966,728 is 14 .
LCM of 586,395 is 231470.
The greatest common factor of 966/586,728/395 = [GCF of 966,728]/[LCM of 586,395]= 14/231470
Therefore, the GCF of 966/586,728/395 is 14/231470.
To find the highest common factor of 966,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 966,728 is 14.
Lets's calculate GCF of 966,728
2 | 966, 728 |
7 | 483, 364 |
69, 52 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 966,728 . The biggest common factor number is the GCF number.
So the greatest common factor 966,728 is 14.
Lets's calculate LCM of 586,395
Given numbers has no common factors except 1. So, there LCM is their product i.e 231470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/231470
Therefore, the GCF of Fractions 966/586,728/395 is 14/231470
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 586,395 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,395) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(586,395) x common factors =1 x 1 = 1
LCM(586,395) = ( 586 × 395 ) / 1
LCM(586,395) = 231470 / 1
LCM(586,395) = 231470
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 966,728?
The HCF of 966,728 is 14
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 966/586, 728/395?
Answer: GCF of Numerators as per given numbers 966/586, 728/395 is
GCF of Numerators i.e. for 966,728 is 14
LCM of denominators i.e. for 586,395 is 231470.
Thus, GCF of Fractions is 14/231470.Finally, GCF of Fractions for 966/586, 728/395 is 14/231470.