Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 18/90,12/57,309/513
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 18,12,309
Greatest Common Factor of Numerators i.e. GCF of 18,12,309 is 3 .
LCM of Denominators means LCM of 90,57,513 as per the given fractions.
LCM of 90,57,513 is 5130 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 18,12,309
3 | 18, 12, 309 |
6, 4, 103 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1,2,3,6,9,18
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 309
List of positive integer factors of 309 that divides 309 without a remainder.
1,3,103,309
Greatest Common Factor
We found the factors 18,12,309 . The biggest common factor number is the GCF number.
So the greatest common factor 18,12,309 is 3.
Lets's calculate LCM of 90,57,513
3 | 90, 57, 513 |
3 | 30, 19, 171 |
19 | 10, 19, 57 |
10, 1, 3 |
∴ So the LCM of the given numbers is 3 x 3 x 19 x 10 x 1 x 3 = 5130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/5130
Therefore, the GCF of Fractions 18/90,12/57,309/513 is 3/5130
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 90,57,513 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,57,513) = 3
common factors(in case of two or more numbers have common factors) = 171
GCF(90,57,513) x common factors =3 x 171 = 513
LCM(90,57,513) = ( 90 × 57 × 513 ) / 513
LCM(90,57,513) = 2631690 / 513
LCM(90,57,513) = 5130
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 18/90, 12/57, 309/513?
Answer: GCF of Numerators as per given numbers 18/90, 12/57, 309/513 is
GCF of Numerators i.e. for 18,12,309 is 3
LCM of denominators i.e. for 90,57,513 is 5130.
Thus, GCF of Fractions is 3/5130.Finally, GCF of Fractions for 18/90, 12/57, 309/513 is 3/5130.