Use our free GCF of Fractions Calculator tool to compute the GCF of 287/609, 410/384 i.e 41/77952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/609, 410/384.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 287/609,410/384
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 287/609,410/384, numerators are 287,410
Denominators are 609,384
The GCF of 287,410 is 41 .
LCM of 609,384 is 77952.
The greatest common factor of 287/609,410/384 = [GCF of 287,410]/[LCM of 609,384]= 41/77952
Therefore, the GCF of 287/609,410/384 is 41/77952.
To find the highest common factor of 287,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 287 are 1, 7, 41, 287
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 287,410 is 41.
Lets's calculate GCF of 287,410
41 | 287, 410 |
7, 10 |
∴ So the GCF of the given numbers is 41 = 41
Now, list down the factors of 287
:1,7,41,287
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 287,410 . The biggest common factor number is the GCF number.
So the greatest common factor 287,410 is 41.
Lets's calculate LCM of 609,384
3 | 609, 384 |
203, 128 |
∴ So the LCM of the given numbers is 3 x 203 x 128 = 77952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/77952
Therefore, the GCF of Fractions 287/609,410/384 is 41/77952
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 609,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(609,384) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(609,384) x common factors =3 x 1 = 3
LCM(609,384) = ( 609 × 384 ) / 3
LCM(609,384) = 233856 / 3
LCM(609,384) = 77952
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 287,410?
The HCF of 287,410 is 41
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 287/609, 410/384?
Answer: GCF of Numerators as per given numbers 287/609, 410/384 is
GCF of Numerators i.e. for 287,410 is 41
LCM of denominators i.e. for 609,384 is 77952.
Thus, GCF of Fractions is 41/77952.Finally, GCF of Fractions for 287/609, 410/384 is 41/77952.