Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1698/514,9735/814
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 1698,9735
Greatest Common Factor of Numerators i.e. GCF of 1698,9735 is 3 .
LCM of Denominators means LCM of 514,814 as per the given fractions.
LCM of 514,814 is 209198 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 1698,9735
3 | 1698, 9735 |
566, 3245 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 1698
List of positive integer factors of 1698 that divides 1698 without a remainder.
1,2,3,6,283,566,849,1698
Factors of 9735
List of positive integer factors of 9735 that divides 9735 without a remainder.
1,3,5,11,15,33,55,59,165,177,295,649,885,1947,3245,9735
Greatest Common Factor
We found the factors 1698,9735 . The biggest common factor number is the GCF number.
So the greatest common factor 1698,9735 is 3.
Lets's calculate LCM of 514,814
2 | 514, 814 |
257, 407 |
∴ So the LCM of the given numbers is 2 x 257 x 407 = 209198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/209198
Therefore, the GCF of Fractions 1698/514,9735/814 is 3/209198
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 514,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(514,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(514,814) x common factors =2 x 1 = 2
LCM(514,814) = ( 514 × 814 ) / 2
LCM(514,814) = 418396 / 2
LCM(514,814) = 209198
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 1698/514, 9735/814?
Answer: GCF of Numerators as per given numbers 1698/514, 9735/814 is
GCF of Numerators i.e. for 1698,9735 is 3
LCM of denominators i.e. for 514,814 is 209198.
Thus, GCF of Fractions is 3/209198.Finally, GCF of Fractions for 1698/514, 9735/814 is 3/209198.