Use our free GCF of Fractions Calculator tool to compute the GCF of 304/774, 864/327 i.e 16/84366 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/774, 864/327.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 304/774,864/327
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 304/774,864/327, numerators are 304,864
Denominators are 774,327
The GCF of 304,864 is 16 .
LCM of 774,327 is 84366.
The greatest common factor of 304/774,864/327 = [GCF of 304,864]/[LCM of 774,327]= 16/84366
Therefore, the GCF of 304/774,864/327 is 16/84366.
To find the highest common factor of 304,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 304,864 is 16.
Lets's calculate GCF of 304,864
2 | 304, 864 |
2 | 152, 432 |
2 | 76, 216 |
2 | 38, 108 |
19, 54 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 304,864 . The biggest common factor number is the GCF number.
So the greatest common factor 304,864 is 16.
Lets's calculate LCM of 774,327
3 | 774, 327 |
258, 109 |
∴ So the LCM of the given numbers is 3 x 258 x 109 = 84366
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/84366
Therefore, the GCF of Fractions 304/774,864/327 is 16/84366
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 774,327 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(774,327) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(774,327) x common factors =3 x 1 = 3
LCM(774,327) = ( 774 × 327 ) / 3
LCM(774,327) = 253098 / 3
LCM(774,327) = 84366
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 304,864?
The HCF of 304,864 is 16
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 304/774, 864/327?
Answer: GCF of Numerators as per given numbers 304/774, 864/327 is
GCF of Numerators i.e. for 304,864 is 16
LCM of denominators i.e. for 774,327 is 84366.
Thus, GCF of Fractions is 16/84366.Finally, GCF of Fractions for 304/774, 864/327 is 16/84366.