Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 20/39,16/24,12/36,35/36
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 20,16,12,35
Greatest Common Factor of Numerators i.e. GCF of 20,16,12,35 is 1 .
LCM of Denominators means LCM of 39,24,36,36 as per the given fractions.
LCM of 39,24,36,36 is 936 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 20,16,12,35
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1,2,4,5,10,20
Factors of 16
List of positive integer factors of 16 that divides 16 without a remainder.
1,2,4,8,16
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Greatest Common Factor
We found the factors 20,16,12,35 . The biggest common factor number is the GCF number.
So the greatest common factor 20,16,12,35 is 1.
Lets's calculate LCM of 39,24,36,36
2 | 39, 24, 36, 36 |
2 | 39, 12, 18, 18 |
3 | 39, 6, 9, 9 |
3 | 13, 2, 3, 3 |
13, 2, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 13 x 2 x 1 x 1 = 936
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/936
Therefore, the GCF of Fractions 20/39,16/24,12/36,35/36 is 1/936
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 39,24,36,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,24,36,36) = 3
common factors(in case of two or more numbers have common factors) = 432
GCF(39,24,36,36) x common factors =3 x 432 = 1296
LCM(39,24,36,36) = ( 39 × 24 × 36 × 36 ) / 1296
LCM(39,24,36,36) = 1213056 / 1296
LCM(39,24,36,36) = 936
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 20/39, 16/24, 12/36, 35/36?
Answer: GCF of Numerators as per given numbers 20/39, 16/24, 12/36, 35/36 is
GCF of Numerators i.e. for 20,16,12,35 is 1
LCM of denominators i.e. for 39,24,36,36 is 936.
Thus, GCF of Fractions is 1/936.Finally, GCF of Fractions for 20/39, 16/24, 12/36, 35/36 is 1/936.