Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 41/58,43/15,89/75,56/18
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 41,43,89,56
Greatest Common Factor of Numerators i.e. GCF of 41,43,89,56 is 1 .
LCM of Denominators means LCM of 58,15,75,18 as per the given fractions.
LCM of 58,15,75,18 is 13050 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 41,43,89,56
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1,41
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 56
List of positive integer factors of 56 that divides 56 without a remainder.
1,2,4,7,8,14,28,56
Greatest Common Factor
We found the factors 41,43,89,56 . The biggest common factor number is the GCF number.
So the greatest common factor 41,43,89,56 is 1.
Lets's calculate LCM of 58,15,75,18
2 | 58, 15, 75, 18 |
3 | 29, 15, 75, 9 |
5 | 29, 5, 25, 3 |
29, 1, 5, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 29 x 1 x 5 x 3 = 13050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13050
Therefore, the GCF of Fractions 41/58,43/15,89/75,56/18 is 1/13050
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 58,15,75,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(58,15,75,18) = 1
common factors(in case of two or more numbers have common factors) = 90
GCF(58,15,75,18) x common factors =1 x 90 = 90
LCM(58,15,75,18) = ( 58 × 15 × 75 × 18 ) / 90
LCM(58,15,75,18) = 1174500 / 90
LCM(58,15,75,18) = 13050
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 41/58, 43/15, 89/75, 56/18?
Answer: GCF of Numerators as per given numbers 41/58, 43/15, 89/75, 56/18 is
GCF of Numerators i.e. for 41,43,89,56 is 1
LCM of denominators i.e. for 58,15,75,18 is 13050.
Thus, GCF of Fractions is 1/13050.Finally, GCF of Fractions for 41/58, 43/15, 89/75, 56/18 is 1/13050.