Use our free GCF of Fractions Calculator tool to compute the GCF of 675/131, 864/575 i.e 27/75325 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/131, 864/575.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 675/131,864/575
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 675/131,864/575, numerators are 675,864
Denominators are 131,575
The GCF of 675,864 is 27 .
LCM of 131,575 is 75325.
The greatest common factor of 675/131,864/575 = [GCF of 675,864]/[LCM of 131,575]= 27/75325
Therefore, the GCF of 675/131,864/575 is 27/75325.
To find the highest common factor of 675,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
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 675,864 is 27.
Lets's calculate GCF of 675,864
3 | 675, 864 |
3 | 225, 288 |
3 | 75, 96 |
25, 32 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
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 675,864 . The biggest common factor number is the GCF number.
So the greatest common factor 675,864 is 27.
Lets's calculate LCM of 131,575
Given numbers has no common factors except 1. So, there LCM is their product i.e 75325
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/75325
Therefore, the GCF of Fractions 675/131,864/575 is 27/75325
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 131,575 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(131,575) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(131,575) x common factors =1 x 1 = 1
LCM(131,575) = ( 131 × 575 ) / 1
LCM(131,575) = 75325 / 1
LCM(131,575) = 75325
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 675,864?
The HCF of 675,864 is 27
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 675/131, 864/575?
Answer: GCF of Numerators as per given numbers 675/131, 864/575 is
GCF of Numerators i.e. for 675,864 is 27
LCM of denominators i.e. for 131,575 is 75325.
Thus, GCF of Fractions is 27/75325.Finally, GCF of Fractions for 675/131, 864/575 is 27/75325.