Use our free GCF of Fractions Calculator tool to compute the GCF of 777/460, 135/208 i.e 3/23920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 777/460, 135/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 777/460,135/208
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 777/460,135/208, numerators are 777,135
Denominators are 460,208
The GCF of 777,135 is 3 .
LCM of 460,208 is 23920.
The greatest common factor of 777/460,135/208 = [GCF of 777,135]/[LCM of 460,208]= 3/23920
Therefore, the GCF of 777/460,135/208 is 3/23920.
To find the highest common factor of 777,135, we have to find the factors of both numbers and list the highest common factor.
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The HCF of 777,135 is 3.
Lets's calculate GCF of 777,135
3 | 777, 135 |
259, 45 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Greatest Common Factor
We found the factors 777,135 . The biggest common factor number is the GCF number.
So the greatest common factor 777,135 is 3.
Lets's calculate LCM of 460,208
2 | 460, 208 |
2 | 230, 104 |
115, 52 |
∴ So the LCM of the given numbers is 2 x 2 x 115 x 52 = 23920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/23920
Therefore, the GCF of Fractions 777/460,135/208 is 3/23920
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 460,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(460,208) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(460,208) x common factors =4 x 1 = 4
LCM(460,208) = ( 460 × 208 ) / 4
LCM(460,208) = 95680 / 4
LCM(460,208) = 23920
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 777,135?
The HCF of 777,135 is 3
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 777/460, 135/208?
Answer: GCF of Numerators as per given numbers 777/460, 135/208 is
GCF of Numerators i.e. for 777,135 is 3
LCM of denominators i.e. for 460,208 is 23920.
Thus, GCF of Fractions is 3/23920.Finally, GCF of Fractions for 777/460, 135/208 is 3/23920.