Use our free GCF of Fractions Calculator tool to compute the GCF of 850/837, 2170/418 i.e 10/349866 easily. The following is the detailed procedure to determine the greatest common factor of fractions 850/837, 2170/418.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 850/837,2170/418
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 850/837,2170/418, numerators are 850,2170
Denominators are 837,418
The GCF of 850,2170 is 10 .
LCM of 837,418 is 349866.
The greatest common factor of 850/837,2170/418 = [GCF of 850,2170]/[LCM of 837,418]= 10/349866
Therefore, the GCF of 850/837,2170/418 is 10/349866.
To find the highest common factor of 850,2170, we have to find the factors of both numbers and list the highest common factor.
The factors of 850 are 1, 2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850
The factors of 2170 are 1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085, 2170
The HCF of 850,2170 is 10.
Lets's calculate GCF of 850,2170
2 | 850, 2170 |
5 | 425, 1085 |
85, 217 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Now, list down the factors of 850
:1,2,5,10,17,25,34,50,85,170,425,850
Now, list down the factors of 2170
:1,2,5,7,10,14,31,35,62,70,155,217,310,434,1085,2170
Greatest Common Factor
We found the factors 850,2170 . The biggest common factor number is the GCF number.
So the greatest common factor 850,2170 is 10.
Lets's calculate LCM of 837,418
Given numbers has no common factors except 1. So, there LCM is their product i.e 349866
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/349866
Therefore, the GCF of Fractions 850/837,2170/418 is 10/349866
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 837,418 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(837,418) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(837,418) x common factors =1 x 1 = 1
LCM(837,418) = ( 837 × 418 ) / 1
LCM(837,418) = 349866 / 1
LCM(837,418) = 349866
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 850,2170?
The HCF of 850,2170 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 850/837, 2170/418?
Answer: GCF of Numerators as per given numbers 850/837, 2170/418 is
GCF of Numerators i.e. for 850,2170 is 10
LCM of denominators i.e. for 837,418 is 349866.
Thus, GCF of Fractions is 10/349866.Finally, GCF of Fractions for 850/837, 2170/418 is 10/349866.