Use our free GCF of Fractions Calculator tool to compute the GCF of 870/734, 850/540 i.e 10/198180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 870/734, 850/540.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 870/734,850/540
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 870/734,850/540, numerators are 870,850
Denominators are 734,540
The GCF of 870,850 is 10 .
LCM of 734,540 is 198180.
The greatest common factor of 870/734,850/540 = [GCF of 870,850]/[LCM of 734,540]= 10/198180
Therefore, the GCF of 870/734,850/540 is 10/198180.
To find the highest common factor of 870,850, we have to find the factors of both numbers and list the highest common factor.
The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870
The factors of 850 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850
The HCF of 870,850 is 10.
Lets's calculate GCF of 870,850
2 | 870, 850 |
5 | 435, 425 |
87, 85 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 870
:1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870
Now, list down the factors of 850
:1,2,5,10,17,25,34,50,85,170,425,850
Greatest Common Factor
We found the factors 870,850 . The biggest common factor number is the GCF number.
So the greatest common factor 870,850 is 10.
Lets's calculate LCM of 734,540
2 | 734, 540 |
367, 270 |
∴ So the LCM of the given numbers is 2 x 367 x 270 = 198180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/198180
Therefore, the GCF of Fractions 870/734,850/540 is 10/198180
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 734,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(734,540) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(734,540) x common factors =2 x 1 = 2
LCM(734,540) = ( 734 × 540 ) / 2
LCM(734,540) = 396360 / 2
LCM(734,540) = 198180
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 870,850?
The HCF of 870,850 is 10
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 870/734, 850/540?
Answer: GCF of Numerators as per given numbers 870/734, 850/540 is
GCF of Numerators i.e. for 870,850 is 10
LCM of denominators i.e. for 734,540 is 198180.
Thus, GCF of Fractions is 10/198180.Finally, GCF of Fractions for 870/734, 850/540 is 10/198180.