Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/60,89/21,96/42,913/46
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 40,89,96,913
Greatest Common Factor of Numerators i.e. GCF of 40,89,96,913 is 1 .
LCM of Denominators means LCM of 60,21,42,46 as per the given fractions.
LCM of 60,21,42,46 is 9660 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 40,89,96,913
∴ So GCF of numbers is 1 because of no common factors present between them.
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 89
List of positive integer factors of 89 that divides 89 without a remainder.
1,89
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 913
List of positive integer factors of 913 that divides 913 without a remainder.
1,11,83,913
Greatest Common Factor
We found the factors 40,89,96,913 . The biggest common factor number is the GCF number.
So the greatest common factor 40,89,96,913 is 1.
Lets's calculate LCM of 60,21,42,46
2 | 60, 21, 42, 46 |
3 | 30, 21, 21, 23 |
7 | 10, 7, 7, 23 |
10, 1, 1, 23 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 10 x 1 x 1 x 23 = 9660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9660
Therefore, the GCF of Fractions 40/60,89/21,96/42,913/46 is 1/9660
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 60,21,42,46 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,21,42,46) = 1
common factors(in case of two or more numbers have common factors) = 252
GCF(60,21,42,46) x common factors =1 x 252 = 252
LCM(60,21,42,46) = ( 60 × 21 × 42 × 46 ) / 252
LCM(60,21,42,46) = 2434320 / 252
LCM(60,21,42,46) = 9660
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 40/60, 89/21, 96/42, 913/46?
Answer: GCF of Numerators as per given numbers 40/60, 89/21, 96/42, 913/46 is
GCF of Numerators i.e. for 40,89,96,913 is 1
LCM of denominators i.e. for 60,21,42,46 is 9660.
Thus, GCF of Fractions is 1/9660.Finally, GCF of Fractions for 40/60, 89/21, 96/42, 913/46 is 1/9660.