Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/75,78/67,74/43,50/499
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 40,78,74,50
Greatest Common Factor of Numerators i.e. GCF of 40,78,74,50 is 2 .
LCM of Denominators means LCM of 75,67,43,499 as per the given fractions.
LCM of 75,67,43,499 is 107821425 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 40,78,74,50
2 | 40, 78, 74, 50 |
20, 39, 37, 25 |
∴ So the GCF of the given numbers is 2 = 2
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 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1,2,5,10,25,50
Greatest Common Factor
We found the factors 40,78,74,50 . The biggest common factor number is the GCF number.
So the greatest common factor 40,78,74,50 is 2.
Lets's calculate LCM of 75,67,43,499
Given numbers has no common factors except 1. So, there LCM is their product i.e 107821425
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/107821425
Therefore, the GCF of Fractions 40/75,78/67,74/43,50/499 is 2/107821425
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 75,67,43,499 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,67,43,499) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,67,43,499) x common factors =1 x 1 = 1
LCM(75,67,43,499) = ( 75 × 67 × 43 × 499 ) / 1
LCM(75,67,43,499) = 107821425 / 1
LCM(75,67,43,499) = 107821425
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 40/75, 78/67, 74/43, 50/499?
Answer: GCF of Numerators as per given numbers 40/75, 78/67, 74/43, 50/499 is
GCF of Numerators i.e. for 40,78,74,50 is 2
LCM of denominators i.e. for 75,67,43,499 is 107821425.
Thus, GCF of Fractions is 2/107821425.Finally, GCF of Fractions for 40/75, 78/67, 74/43, 50/499 is 2/107821425.