Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 36/43,96/39,728/42
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 36,96,728
Greatest Common Factor of Numerators i.e. GCF of 36,96,728 is 4 .
LCM of Denominators means LCM of 43,39,42 as per the given fractions.
LCM of 43,39,42 is 23478 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 36,96,728
2 | 36, 96, 728 |
2 | 18, 48, 364 |
9, 24, 182 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1,2,3,4,6,9,12,18,36
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 728
List of positive integer factors of 728 that divides 728 without a remainder.
1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 36,96,728 . The biggest common factor number is the GCF number.
So the greatest common factor 36,96,728 is 4.
Lets's calculate LCM of 43,39,42
3 | 43, 39, 42 |
43, 13, 14 |
∴ So the LCM of the given numbers is 3 x 43 x 13 x 14 = 23478
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/23478
Therefore, the GCF of Fractions 36/43,96/39,728/42 is 4/23478
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 43,39,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(43,39,42) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(43,39,42) x common factors =1 x 3 = 3
LCM(43,39,42) = ( 43 × 39 × 42 ) / 3
LCM(43,39,42) = 70434 / 3
LCM(43,39,42) = 23478
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 36/43, 96/39, 728/42?
Answer: GCF of Numerators as per given numbers 36/43, 96/39, 728/42 is
GCF of Numerators i.e. for 36,96,728 is 4
LCM of denominators i.e. for 43,39,42 is 23478.
Thus, GCF of Fractions is 4/23478.Finally, GCF of Fractions for 36/43, 96/39, 728/42 is 4/23478.