Use our free GCF of Fractions Calculator tool to compute the GCF of 864/605, 576/129 i.e 288/78045 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/605, 576/129.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 864/605,576/129
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 864/605,576/129, numerators are 864,576
Denominators are 605,129
The GCF of 864,576 is 288 .
LCM of 605,129 is 78045.
The greatest common factor of 864/605,576/129 = [GCF of 864,576]/[LCM of 605,129]= 288/78045
Therefore, the GCF of 864/605,576/129 is 288/78045.
To find the highest common factor of 864,576, we have to find the factors of both numbers and list the highest common factor.
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 factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The HCF of 864,576 is 288.
Lets's calculate GCF of 864,576
2 | 864, 576 |
2 | 432, 288 |
2 | 216, 144 |
2 | 108, 72 |
2 | 54, 36 |
3 | 27, 18 |
3 | 9, 6 |
3, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
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
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
Greatest Common Factor
We found the factors 864,576 . The biggest common factor number is the GCF number.
So the greatest common factor 864,576 is 288.
Lets's calculate LCM of 605,129
Given numbers has no common factors except 1. So, there LCM is their product i.e 78045
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 288/78045
Therefore, the GCF of Fractions 864/605,576/129 is 288/78045
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 605,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(605,129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(605,129) x common factors =1 x 1 = 1
LCM(605,129) = ( 605 × 129 ) / 1
LCM(605,129) = 78045 / 1
LCM(605,129) = 78045
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 864,576?
The HCF of 864,576 is 288
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 864/605, 576/129?
Answer: GCF of Numerators as per given numbers 864/605, 576/129 is
GCF of Numerators i.e. for 864,576 is 288
LCM of denominators i.e. for 605,129 is 78045.
Thus, GCF of Fractions is 288/78045.Finally, GCF of Fractions for 864/605, 576/129 is 288/78045.