Use our free GCF of Fractions Calculator tool to compute the GCF of 398/311, 623/409 i.e 1/127199 easily. The following is the detailed procedure to determine the greatest common factor of fractions 398/311, 623/409.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 398/311,623/409
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 398/311,623/409, numerators are 398,623
Denominators are 311,409
The GCF of 398,623 is 1 .
LCM of 311,409 is 127199.
The greatest common factor of 398/311,623/409 = [GCF of 398,623]/[LCM of 311,409]= 1/127199
Therefore, the GCF of 398/311,623/409 is 1/127199.
To find the highest common factor of 398,623, we have to find the factors of both numbers and list the highest common factor.
The factors of 398 are 1, 2, 199, 398
The factors of 623 are 1, 7, 89, 623
The HCF of 398,623 is 1.
Lets's calculate GCF of 398,623
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 623
:1,7,89,623
Greatest Common Factor
We found the factors 398,623 . The biggest common factor number is the GCF number.
So the greatest common factor 398,623 is 1.
Lets's calculate LCM of 311,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 127199
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127199
Therefore, the GCF of Fractions 398/311,623/409 is 1/127199
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 311,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(311,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(311,409) x common factors =1 x 1 = 1
LCM(311,409) = ( 311 × 409 ) / 1
LCM(311,409) = 127199 / 1
LCM(311,409) = 127199
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 398,623?
The HCF of 398,623 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 398/311, 623/409?
Answer: GCF of Numerators as per given numbers 398/311, 623/409 is
GCF of Numerators i.e. for 398,623 is 1
LCM of denominators i.e. for 311,409 is 127199.
Thus, GCF of Fractions is 1/127199.Finally, GCF of Fractions for 398/311, 623/409 is 1/127199.