Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/90,31/81,62/84,44/30
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 30,31,62,44
Greatest Common Factor of Numerators i.e. GCF of 30,31,62,44 is 1 .
LCM of Denominators means LCM of 90,81,84,30 as per the given fractions.
LCM of 90,81,84,30 is 11340 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 30,31,62,44
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 31
List of positive integer factors of 31 that divides 31 without a remainder.
1,31
Factors of 62
List of positive integer factors of 62 that divides 62 without a remainder.
1,2,31,62
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
Greatest Common Factor
We found the factors 30,31,62,44 . The biggest common factor number is the GCF number.
So the greatest common factor 30,31,62,44 is 1.
Lets's calculate LCM of 90,81,84,30
2 | 90, 81, 84, 30 |
3 | 45, 81, 42, 15 |
3 | 5, 27, 14, 15 |
5 | 5, 9, 14, 5 |
1, 9, 14, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 9 x 14 x 1 = 11340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11340
Therefore, the GCF of Fractions 30/90,31/81,62/84,44/30 is 1/11340
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 90,81,84,30 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,81,84,30) = 3
common factors(in case of two or more numbers have common factors) = 540
GCF(90,81,84,30) x common factors =3 x 540 = 1620
LCM(90,81,84,30) = ( 90 × 81 × 84 × 30 ) / 1620
LCM(90,81,84,30) = 18370800 / 1620
LCM(90,81,84,30) = 11340
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 30/90, 31/81, 62/84, 44/30?
Answer: GCF of Numerators as per given numbers 30/90, 31/81, 62/84, 44/30 is
GCF of Numerators i.e. for 30,31,62,44 is 1
LCM of denominators i.e. for 90,81,84,30 is 11340.
Thus, GCF of Fractions is 1/11340.Finally, GCF of Fractions for 30/90, 31/81, 62/84, 44/30 is 1/11340.