Use our free GCF of Fractions Calculator tool to compute the GCF of 387/393, 774/129 i.e 387/16899 easily. The following is the detailed procedure to determine the greatest common factor of fractions 387/393, 774/129.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 387/393,774/129
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 387/393,774/129, numerators are 387,774
Denominators are 393,129
The GCF of 387,774 is 387 .
LCM of 393,129 is 16899.
The greatest common factor of 387/393,774/129 = [GCF of 387,774]/[LCM of 393,129]= 387/16899
Therefore, the GCF of 387/393,774/129 is 387/16899.
To find the highest common factor of 387,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 387 are 1, 3, 9, 43, 129, 387
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 387,774 is 387.
Lets's calculate GCF of 387,774
3 | 387, 774 |
3 | 129, 258 |
43 | 43, 86 |
1, 2 |
∴ So the GCF of the given numbers is 3 x 3 x 43 = 387
Now, list down the factors of 387
:1,3,9,43,129,387
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 387,774 . The biggest common factor number is the GCF number.
So the greatest common factor 387,774 is 387.
Lets's calculate LCM of 393,129
3 | 393, 129 |
131, 43 |
∴ So the LCM of the given numbers is 3 x 131 x 43 = 16899
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 387/16899
Therefore, the GCF of Fractions 387/393,774/129 is 387/16899
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 393,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(393,129) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(393,129) x common factors =3 x 1 = 3
LCM(393,129) = ( 393 × 129 ) / 3
LCM(393,129) = 50697 / 3
LCM(393,129) = 16899
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 387,774?
The HCF of 387,774 is 387
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 387/393, 774/129?
Answer: GCF of Numerators as per given numbers 387/393, 774/129 is
GCF of Numerators i.e. for 387,774 is 387
LCM of denominators i.e. for 393,129 is 16899.
Thus, GCF of Fractions is 387/16899.Finally, GCF of Fractions for 387/393, 774/129 is 387/16899.