Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 185/68,311/62,165/17
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 185,311,165
Greatest Common Factor of Numerators i.e. GCF of 185,311,165 is 1 .
LCM of Denominators means LCM of 68,62,17 as per the given fractions.
LCM of 68,62,17 is 2108 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 185,311,165
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 185
List of positive integer factors of 185 that divides 185 without a remainder.
1,5,37,185
Factors of 311
List of positive integer factors of 311 that divides 311 without a remainder.
1,311
Factors of 165
List of positive integer factors of 165 that divides 165 without a remainder.
1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 185,311,165 . The biggest common factor number is the GCF number.
So the greatest common factor 185,311,165 is 1.
Lets's calculate LCM of 68,62,17
2 | 68, 62, 17 |
17 | 34, 31, 17 |
2, 31, 1 |
∴ So the LCM of the given numbers is 2 x 17 x 2 x 31 x 1 = 2108
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2108
Therefore, the GCF of Fractions 185/68,311/62,165/17 is 1/2108
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 68,62,17 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,62,17) = 1
common factors(in case of two or more numbers have common factors) = 34
GCF(68,62,17) x common factors =1 x 34 = 34
LCM(68,62,17) = ( 68 × 62 × 17 ) / 34
LCM(68,62,17) = 71672 / 34
LCM(68,62,17) = 2108
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 185/68, 311/62, 165/17?
Answer: GCF of Numerators as per given numbers 185/68, 311/62, 165/17 is
GCF of Numerators i.e. for 185,311,165 is 1
LCM of denominators i.e. for 68,62,17 is 2108.
Thus, GCF of Fractions is 1/2108.Finally, GCF of Fractions for 185/68, 311/62, 165/17 is 1/2108.