Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/30,43/61,25/67,40/720
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 23,43,25,40
Greatest Common Factor of Numerators i.e. GCF of 23,43,25,40 is 1 .
LCM of Denominators means LCM of 30,61,67,720 as per the given fractions.
LCM of 30,61,67,720 is 2942640 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 23,43,25,40
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Greatest Common Factor
We found the factors 23,43,25,40 . The biggest common factor number is the GCF number.
So the greatest common factor 23,43,25,40 is 1.
Lets's calculate LCM of 30,61,67,720
2 | 30, 61, 67, 720 |
3 | 15, 61, 67, 360 |
5 | 5, 61, 67, 120 |
1, 61, 67, 24 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 61 x 67 x 24 = 2942640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2942640
Therefore, the GCF of Fractions 23/30,43/61,25/67,40/720 is 1/2942640
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 30,61,67,720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,61,67,720) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(30,61,67,720) x common factors =1 x 30 = 30
LCM(30,61,67,720) = ( 30 × 61 × 67 × 720 ) / 30
LCM(30,61,67,720) = 88279200 / 30
LCM(30,61,67,720) = 2942640
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 23/30, 43/61, 25/67, 40/720?
Answer: GCF of Numerators as per given numbers 23/30, 43/61, 25/67, 40/720 is
GCF of Numerators i.e. for 23,43,25,40 is 1
LCM of denominators i.e. for 30,61,67,720 is 2942640.
Thus, GCF of Fractions is 1/2942640.Finally, GCF of Fractions for 23/30, 43/61, 25/67, 40/720 is 1/2942640.