Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/43,27/82,71/61,82/315
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 27,27,71,82
Greatest Common Factor of Numerators i.e. GCF of 27,27,71,82 is 1 .
LCM of Denominators means LCM of 43,82,61,315 as per the given fractions.
LCM of 43,82,61,315 is 67752090 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 27,27,71,82
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 82
List of positive integer factors of 82 that divides 82 without a remainder.
1,2,41,82
Greatest Common Factor
We found the factors 27,27,71,82 . The biggest common factor number is the GCF number.
So the greatest common factor 27,27,71,82 is 1.
Lets's calculate LCM of 43,82,61,315
Given numbers has no common factors except 1. So, there LCM is their product i.e 67752090
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67752090
Therefore, the GCF of Fractions 27/43,27/82,71/61,82/315 is 1/67752090
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 43,82,61,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(43,82,61,315) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(43,82,61,315) x common factors =1 x 1 = 1
LCM(43,82,61,315) = ( 43 × 82 × 61 × 315 ) / 1
LCM(43,82,61,315) = 67752090 / 1
LCM(43,82,61,315) = 67752090
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 27/43, 27/82, 71/61, 82/315?
Answer: GCF of Numerators as per given numbers 27/43, 27/82, 71/61, 82/315 is
GCF of Numerators i.e. for 27,27,71,82 is 1
LCM of denominators i.e. for 43,82,61,315 is 67752090.
Thus, GCF of Fractions is 1/67752090.Finally, GCF of Fractions for 27/43, 27/82, 71/61, 82/315 is 1/67752090.