Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 44/75,57/36,24/27,91/32
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 44,57,24,91
Greatest Common Factor of Numerators i.e. GCF of 44,57,24,91 is 1 .
LCM of Denominators means LCM of 75,36,27,32 as per the given fractions.
LCM of 75,36,27,32 is 21600 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 44,57,24,91
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 44
List of positive integer factors of 44 that divides 44 without a remainder.
1,2,4,11,22,44
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Factors of 24
List of positive integer factors of 24 that divides 24 without a remainder.
1,2,3,4,6,8,12,24
Factors of 91
List of positive integer factors of 91 that divides 91 without a remainder.
1,7,13,91
Greatest Common Factor
We found the factors 44,57,24,91 . The biggest common factor number is the GCF number.
So the greatest common factor 44,57,24,91 is 1.
Lets's calculate LCM of 75,36,27,32
2 | 75, 36, 27, 32 |
2 | 75, 18, 27, 16 |
3 | 75, 9, 27, 8 |
3 | 25, 3, 9, 8 |
25, 1, 3, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 25 x 1 x 3 x 8 = 21600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21600
Therefore, the GCF of Fractions 44/75,57/36,24/27,91/32 is 1/21600
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 75,36,27,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,36,27,32) = 1
common factors(in case of two or more numbers have common factors) = 108
GCF(75,36,27,32) x common factors =1 x 108 = 108
LCM(75,36,27,32) = ( 75 × 36 × 27 × 32 ) / 108
LCM(75,36,27,32) = 2332800 / 108
LCM(75,36,27,32) = 21600
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 44/75, 57/36, 24/27, 91/32?
Answer: GCF of Numerators as per given numbers 44/75, 57/36, 24/27, 91/32 is
GCF of Numerators i.e. for 44,57,24,91 is 1
LCM of denominators i.e. for 75,36,27,32 is 21600.
Thus, GCF of Fractions is 1/21600.Finally, GCF of Fractions for 44/75, 57/36, 24/27, 91/32 is 1/21600.