Use our free GCF of Fractions Calculator tool to compute the GCF of 30/86, 201/41, 378/108 i.e 3/190404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/86, 201/41, 378/108.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/86,201/41,378/108
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 30/86,201/41,378/108, numerators are 30,201,378
Denominators are 86,41,108
The GCF of 30,201,378 is 3 .
LCM of 86,41,108 is 190404.
The greatest common factor of 30/86,201/41,378/108 = [GCF of 30,201,378]/[LCM of 86,41,108]= 3/190404
Therefore, the GCF of 30/86,201/41,378/108 is 3/190404.
To find the highest common factor of 30,201,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 201 are 1, 3, 67, 201
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 30,201,378 is 3.
Lets's calculate GCF of 30,201,378
3 | 30, 201, 378 |
10, 67, 126 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 201
:1,3,67,201
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 30,201,378 . The biggest common factor number is the GCF number.
So the greatest common factor 30,201,378 is 3.
Lets's calculate LCM of 86,41,108
2 | 86, 41, 108 |
43, 41, 54 |
∴ So the LCM of the given numbers is 2 x 43 x 41 x 54 = 190404
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/190404
Therefore, the GCF of Fractions 30/86,201/41,378/108 is 3/190404
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 86,41,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,41,108) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(86,41,108) x common factors =1 x 2 = 2
LCM(86,41,108) = ( 86 × 41 × 108 ) / 2
LCM(86,41,108) = 380808 / 2
LCM(86,41,108) = 190404
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,201,378?
The HCF of 30,201,378 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 30/86, 201/41, 378/108?
Answer: GCF of Numerators as per given numbers 30/86, 201/41, 378/108 is
GCF of Numerators i.e. for 30,201,378 is 3
LCM of denominators i.e. for 86,41,108 is 190404.
Thus, GCF of Fractions is 3/190404.Finally, GCF of Fractions for 30/86, 201/41, 378/108 is 3/190404.