Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/31,34/73,47/61,30/661
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 40,34,47,30
Greatest Common Factor of Numerators i.e. GCF of 40,34,47,30 is 1 .
LCM of Denominators means LCM of 31,73,61,661 as per the given fractions.
LCM of 31,73,61,661 is 91246423 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 40,34,47,30
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Factors of 47
List of positive integer factors of 47 that divides 47 without a remainder.
1,47
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors 40,34,47,30 . The biggest common factor number is the GCF number.
So the greatest common factor 40,34,47,30 is 1.
Lets's calculate LCM of 31,73,61,661
Given numbers has no common factors except 1. So, there LCM is their product i.e 91246423
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/91246423
Therefore, the GCF of Fractions 40/31,34/73,47/61,30/661 is 1/91246423
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 31,73,61,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,73,61,661) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,73,61,661) x common factors =1 x 1 = 1
LCM(31,73,61,661) = ( 31 × 73 × 61 × 661 ) / 1
LCM(31,73,61,661) = 91246423 / 1
LCM(31,73,61,661) = 91246423
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 40/31, 34/73, 47/61, 30/661?
Answer: GCF of Numerators as per given numbers 40/31, 34/73, 47/61, 30/661 is
GCF of Numerators i.e. for 40,34,47,30 is 1
LCM of denominators i.e. for 31,73,61,661 is 91246423.
Thus, GCF of Fractions is 1/91246423.Finally, GCF of Fractions for 40/31, 34/73, 47/61, 30/661 is 1/91246423.