Use our free GCF of Fractions Calculator tool to compute the GCF of 413/813, 576/591 i.e 1/160161 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/813, 576/591.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 413/813,576/591
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 413/813,576/591, numerators are 413,576
Denominators are 813,591
The GCF of 413,576 is 1 .
LCM of 813,591 is 160161.
The greatest common factor of 413/813,576/591 = [GCF of 413,576]/[LCM of 813,591]= 1/160161
Therefore, the GCF of 413/813,576/591 is 1/160161.
To find the highest common factor of 413,576, we have to find the factors of both numbers and list the highest common factor.
The factors of 413 are 1, 7, 59, 413
The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The HCF of 413,576 is 1.
Lets's calculate GCF of 413,576
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 413
:1,7,59,413
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
Greatest Common Factor
We found the factors 413,576 . The biggest common factor number is the GCF number.
So the greatest common factor 413,576 is 1.
Lets's calculate LCM of 813,591
3 | 813, 591 |
271, 197 |
∴ So the LCM of the given numbers is 3 x 271 x 197 = 160161
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/160161
Therefore, the GCF of Fractions 413/813,576/591 is 1/160161
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 813,591 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(813,591) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(813,591) x common factors =3 x 1 = 3
LCM(813,591) = ( 813 × 591 ) / 3
LCM(813,591) = 480483 / 3
LCM(813,591) = 160161
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 413,576?
The HCF of 413,576 is 1
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 413/813, 576/591?
Answer: GCF of Numerators as per given numbers 413/813, 576/591 is
GCF of Numerators i.e. for 413,576 is 1
LCM of denominators i.e. for 813,591 is 160161.
Thus, GCF of Fractions is 1/160161.Finally, GCF of Fractions for 413/813, 576/591 is 1/160161.