Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 165/14,215/284
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 165,215
Greatest Common Factor of Numerators i.e. GCF of 165,215 is 5 .
LCM of Denominators means LCM of 14,284 as per the given fractions.
LCM of 14,284 is 1988 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 165,215
5 | 165, 215 |
33, 43 |
∴ So the GCF of the given numbers is 5 = 5
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1,3,5,11,15,33,55,165
Factors of 215
List of positive integer factors of 215 that divides 215 without a remainder.
1,5,43,215
Greatest Common Factor
We found the factors 165,215 . The biggest common factor number is the GCF number.
So the greatest common factor 165,215 is 5.
Lets's calculate LCM of 14,284
2 | 14, 284 |
7, 142 |
∴ So the LCM of the given numbers is 2 x 7 x 142 = 1988
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1988
Therefore, the GCF of Fractions 165/14,215/284 is 5/1988
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 14,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,284) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,284) x common factors =2 x 1 = 2
LCM(14,284) = ( 14 × 284 ) / 2
LCM(14,284) = 3976 / 2
LCM(14,284) = 1988
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 165/14, 215/284?
Answer: GCF of Numerators as per given numbers 165/14, 215/284 is
GCF of Numerators i.e. for 165,215 is 5
LCM of denominators i.e. for 14,284 is 1988.
Thus, GCF of Fractions is 5/1988.Finally, GCF of Fractions for 165/14, 215/284 is 5/1988.