Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/90,78/90,387/36
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 30,78,387
Greatest Common Factor of Numerators i.e. GCF of 30,78,387 is 3 .
LCM of Denominators means LCM of 90,90,36 as per the given fractions.
LCM of 90,90,36 is 180 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 30,78,387
3 | 30, 78, 387 |
10, 26, 129 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 387
List of positive integer factors of 387 that divides 387 without a remainder.
1,3,9,43,129,387
Greatest Common Factor
We found the factors 30,78,387 . The biggest common factor number is the GCF number.
So the greatest common factor 30,78,387 is 3.
Lets's calculate LCM of 90,90,36
2 | 90, 90, 36 |
3 | 45, 45, 18 |
3 | 15, 15, 6 |
5 | 5, 5, 2 |
1, 1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 5 x 1 x 1 x 2 = 180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/180
Therefore, the GCF of Fractions 30/90,78/90,387/36 is 3/180
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 90,90,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,90,36) = 18
common factors(in case of two or more numbers have common factors) = 90
GCF(90,90,36) x common factors =18 x 90 = 1620
LCM(90,90,36) = ( 90 × 90 × 36 ) / 1620
LCM(90,90,36) = 291600 / 1620
LCM(90,90,36) = 180
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 30/90, 78/90, 387/36?
Answer: GCF of Numerators as per given numbers 30/90, 78/90, 387/36 is
GCF of Numerators i.e. for 30,78,387 is 3
LCM of denominators i.e. for 90,90,36 is 180.
Thus, GCF of Fractions is 3/180.Finally, GCF of Fractions for 30/90, 78/90, 387/36 is 3/180.