Use our free GCF of Fractions Calculator tool to compute the GCF of 665/271, 560/235 i.e 35/63685 easily. The following is the detailed procedure to determine the greatest common factor of fractions 665/271, 560/235.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 665/271,560/235
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 665/271,560/235, numerators are 665,560
Denominators are 271,235
The GCF of 665,560 is 35 .
LCM of 271,235 is 63685.
The greatest common factor of 665/271,560/235 = [GCF of 665,560]/[LCM of 271,235]= 35/63685
Therefore, the GCF of 665/271,560/235 is 35/63685.
To find the highest common factor of 665,560, we have to find the factors of both numbers and list the highest common factor.
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The HCF of 665,560 is 35.
Lets's calculate GCF of 665,560
5 | 665, 560 |
7 | 133, 112 |
19, 16 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Greatest Common Factor
We found the factors 665,560 . The biggest common factor number is the GCF number.
So the greatest common factor 665,560 is 35.
Lets's calculate LCM of 271,235
Given numbers has no common factors except 1. So, there LCM is their product i.e 63685
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/63685
Therefore, the GCF of Fractions 665/271,560/235 is 35/63685
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 271,235 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(271,235) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(271,235) x common factors =1 x 1 = 1
LCM(271,235) = ( 271 × 235 ) / 1
LCM(271,235) = 63685 / 1
LCM(271,235) = 63685
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 665,560?
The HCF of 665,560 is 35
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 665/271, 560/235?
Answer: GCF of Numerators as per given numbers 665/271, 560/235 is
GCF of Numerators i.e. for 665,560 is 35
LCM of denominators i.e. for 271,235 is 63685.
Thus, GCF of Fractions is 35/63685.Finally, GCF of Fractions for 665/271, 560/235 is 35/63685.