Use our free GCF of Fractions Calculator tool to compute the GCF of 420/994, 660/849 i.e 60/843906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/994, 660/849.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 420/994,660/849
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 420/994,660/849, numerators are 420,660
Denominators are 994,849
The GCF of 420,660 is 60 .
LCM of 994,849 is 843906.
The greatest common factor of 420/994,660/849 = [GCF of 420,660]/[LCM of 994,849]= 60/843906
Therefore, the GCF of 420/994,660/849 is 60/843906.
To find the highest common factor of 420,660, we have to find the factors of both numbers and list the highest common factor.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The HCF of 420,660 is 60.
Lets's calculate GCF of 420,660
2 | 420, 660 |
2 | 210, 330 |
3 | 105, 165 |
5 | 35, 55 |
7, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Greatest Common Factor
We found the factors 420,660 . The biggest common factor number is the GCF number.
So the greatest common factor 420,660 is 60.
Lets's calculate LCM of 994,849
Given numbers has no common factors except 1. So, there LCM is their product i.e 843906
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/843906
Therefore, the GCF of Fractions 420/994,660/849 is 60/843906
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 994,849 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(994,849) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(994,849) x common factors =1 x 1 = 1
LCM(994,849) = ( 994 × 849 ) / 1
LCM(994,849) = 843906 / 1
LCM(994,849) = 843906
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 420,660?
The HCF of 420,660 is 60
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 420/994, 660/849?
Answer: GCF of Numerators as per given numbers 420/994, 660/849 is
GCF of Numerators i.e. for 420,660 is 60
LCM of denominators i.e. for 994,849 is 843906.
Thus, GCF of Fractions is 60/843906.Finally, GCF of Fractions for 420/994, 660/849 is 60/843906.