Use our free GCF of Fractions Calculator tool to compute the GCF of 403/576, 589/329 i.e 31/189504 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/576, 589/329.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 403/576,589/329
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 403/576,589/329, numerators are 403,589
Denominators are 576,329
The GCF of 403,589 is 31 .
LCM of 576,329 is 189504.
The greatest common factor of 403/576,589/329 = [GCF of 403,589]/[LCM of 576,329]= 31/189504
Therefore, the GCF of 403/576,589/329 is 31/189504.
To find the highest common factor of 403,589, we have to find the factors of both numbers and list the highest common factor.
The factors of 403 are 1, 13, 31, 403
The factors of 589 are 1, 19, 31, 589
The HCF of 403,589 is 31.
Lets's calculate GCF of 403,589
31 | 403, 589 |
13, 19 |
∴ So the GCF of the given numbers is 31 = 31
Now, list down the factors of 403
:1,13,31,403
Now, list down the factors of 589
:1,19,31,589
Greatest Common Factor
We found the factors 403,589 . The biggest common factor number is the GCF number.
So the greatest common factor 403,589 is 31.
Lets's calculate LCM of 576,329
Given numbers has no common factors except 1. So, there LCM is their product i.e 189504
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/189504
Therefore, the GCF of Fractions 403/576,589/329 is 31/189504
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 576,329 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,329) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(576,329) x common factors =1 x 1 = 1
LCM(576,329) = ( 576 × 329 ) / 1
LCM(576,329) = 189504 / 1
LCM(576,329) = 189504
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 403,589?
The HCF of 403,589 is 31
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 403/576, 589/329?
Answer: GCF of Numerators as per given numbers 403/576, 589/329 is
GCF of Numerators i.e. for 403,589 is 31
LCM of denominators i.e. for 576,329 is 189504.
Thus, GCF of Fractions is 31/189504.Finally, GCF of Fractions for 403/576, 589/329 is 31/189504.