Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 322/65,431/17,171/289
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 322,431,171
Greatest Common Factor of Numerators i.e. GCF of 322,431,171 is 1 .
LCM of Denominators means LCM of 65,17,289 as per the given fractions.
LCM of 65,17,289 is 18785 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 322,431,171
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 322
List of positive integer factors of 322 that divides 322 without a remainder.
1,2,7,14,23,46,161,322
Factors of 431
List of positive integer factors of 431 that divides 431 without a remainder.
1,431
Factors of 171
List of positive integer factors of 171 that divides 171 without a remainder.
1,3,9,19,57,171
Greatest Common Factor
We found the factors 322,431,171 . The biggest common factor number is the GCF number.
So the greatest common factor 322,431,171 is 1.
Lets's calculate LCM of 65,17,289
17 | 65, 17, 289 |
65, 1, 17 |
∴ So the LCM of the given numbers is 17 x 65 x 1 x 17 = 18785
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18785
Therefore, the GCF of Fractions 322/65,431/17,171/289 is 1/18785
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 65,17,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,17,289) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(65,17,289) x common factors =1 x 17 = 17
LCM(65,17,289) = ( 65 × 17 × 289 ) / 17
LCM(65,17,289) = 319345 / 17
LCM(65,17,289) = 18785
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 322/65, 431/17, 171/289?
Answer: GCF of Numerators as per given numbers 322/65, 431/17, 171/289 is
GCF of Numerators i.e. for 322,431,171 is 1
LCM of denominators i.e. for 65,17,289 is 18785.
Thus, GCF of Fractions is 1/18785.Finally, GCF of Fractions for 322/65, 431/17, 171/289 is 1/18785.