Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 409/289,301/731,305/961
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 409,301,305
Greatest Common Factor of Numerators i.e. GCF of 409,301,305 is 1 .
LCM of Denominators means LCM of 289,731,961 as per the given fractions.
LCM of 289,731,961 is 11942347 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 409,301,305
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 409
List of positive integer factors of 409 that divides 409 without a remainder.
1,409
Factors of 301
List of positive integer factors of 301 that divides 301 without a remainder.
1,7,43,301
Factors of 305
List of positive integer factors of 305 that divides 305 without a remainder.
1,5,61,305
Greatest Common Factor
We found the factors 409,301,305 . The biggest common factor number is the GCF number.
So the greatest common factor 409,301,305 is 1.
Lets's calculate LCM of 289,731,961
17 | 289, 731, 961 |
17, 43, 961 |
∴ So the LCM of the given numbers is 17 x 17 x 43 x 961 = 11942347
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11942347
Therefore, the GCF of Fractions 409/289,301/731,305/961 is 1/11942347
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 289,731,961 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,731,961) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(289,731,961) x common factors =1 x 17 = 17
LCM(289,731,961) = ( 289 × 731 × 961 ) / 17
LCM(289,731,961) = 203019899 / 17
LCM(289,731,961) = 11942347
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 409/289, 301/731, 305/961?
Answer: GCF of Numerators as per given numbers 409/289, 301/731, 305/961 is
GCF of Numerators i.e. for 409,301,305 is 1
LCM of denominators i.e. for 289,731,961 is 11942347.
Thus, GCF of Fractions is 1/11942347.Finally, GCF of Fractions for 409/289, 301/731, 305/961 is 1/11942347.