Use our free GCF of Fractions Calculator tool to compute the GCF of 675/388, 120/291 i.e 15/1164 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/388, 120/291.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 675/388,120/291
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 675/388,120/291, numerators are 675,120
Denominators are 388,291
The GCF of 675,120 is 15 .
LCM of 388,291 is 1164.
The greatest common factor of 675/388,120/291 = [GCF of 675,120]/[LCM of 388,291]= 15/1164
Therefore, the GCF of 675/388,120/291 is 15/1164.
To find the highest common factor of 675,120, 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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 675,120 is 15.
Lets's calculate GCF of 675,120
3 | 675, 120 |
5 | 225, 40 |
45, 8 |
∴ So the GCF of the given numbers is 3 x 5 = 15
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 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 675,120 . The biggest common factor number is the GCF number.
So the greatest common factor 675,120 is 15.
Lets's calculate LCM of 388,291
97 | 388, 291 |
4, 3 |
∴ So the LCM of the given numbers is 97 x 4 x 3 = 1164
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/1164
Therefore, the GCF of Fractions 675/388,120/291 is 15/1164
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 388,291 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(388,291) = 97
common factors(in case of two or more numbers have common factors) = 1
GCF(388,291) x common factors =97 x 1 = 97
LCM(388,291) = ( 388 × 291 ) / 97
LCM(388,291) = 112908 / 97
LCM(388,291) = 1164
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 675,120?
The HCF of 675,120 is 15
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 675/388, 120/291?
Answer: GCF of Numerators as per given numbers 675/388, 120/291 is
GCF of Numerators i.e. for 675,120 is 15
LCM of denominators i.e. for 388,291 is 1164.
Thus, GCF of Fractions is 15/1164.Finally, GCF of Fractions for 675/388, 120/291 is 15/1164.