Use our free GCF of Fractions Calculator tool to compute the GCF of 591/227, 164/312 i.e 1/70824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 591/227, 164/312.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 591/227,164/312
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 591/227,164/312, numerators are 591,164
Denominators are 227,312
The GCF of 591,164 is 1 .
LCM of 227,312 is 70824.
The greatest common factor of 591/227,164/312 = [GCF of 591,164]/[LCM of 227,312]= 1/70824
Therefore, the GCF of 591/227,164/312 is 1/70824.
To find the highest common factor of 591,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 591 are 1, 3, 197, 591
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 591,164 is 1.
Lets's calculate GCF of 591,164
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 591
:1,3,197,591
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 591,164 . The biggest common factor number is the GCF number.
So the greatest common factor 591,164 is 1.
Lets's calculate LCM of 227,312
Given numbers has no common factors except 1. So, there LCM is their product i.e 70824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/70824
Therefore, the GCF of Fractions 591/227,164/312 is 1/70824
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 227,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(227,312) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(227,312) x common factors =1 x 1 = 1
LCM(227,312) = ( 227 × 312 ) / 1
LCM(227,312) = 70824 / 1
LCM(227,312) = 70824
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 591,164?
The HCF of 591,164 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 591/227, 164/312?
Answer: GCF of Numerators as per given numbers 591/227, 164/312 is
GCF of Numerators i.e. for 591,164 is 1
LCM of denominators i.e. for 227,312 is 70824.
Thus, GCF of Fractions is 1/70824.Finally, GCF of Fractions for 591/227, 164/312 is 1/70824.