Use our free GCF of Fractions Calculator tool to compute the GCF of 197/419, 406/740 i.e 1/310060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 197/419, 406/740.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 197/419,406/740
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 197/419,406/740, numerators are 197,406
Denominators are 419,740
The GCF of 197,406 is 1 .
LCM of 419,740 is 310060.
The greatest common factor of 197/419,406/740 = [GCF of 197,406]/[LCM of 419,740]= 1/310060
Therefore, the GCF of 197/419,406/740 is 1/310060.
To find the highest common factor of 197,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 197 are 1, 197
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 197,406 is 1.
Lets's calculate GCF of 197,406
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 197
:1,197
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 197,406 . The biggest common factor number is the GCF number.
So the greatest common factor 197,406 is 1.
Lets's calculate LCM of 419,740
Given numbers has no common factors except 1. So, there LCM is their product i.e 310060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/310060
Therefore, the GCF of Fractions 197/419,406/740 is 1/310060
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 419,740 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,740) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,740) x common factors =1 x 1 = 1
LCM(419,740) = ( 419 × 740 ) / 1
LCM(419,740) = 310060 / 1
LCM(419,740) = 310060
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 197,406?
The HCF of 197,406 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 197/419, 406/740?
Answer: GCF of Numerators as per given numbers 197/419, 406/740 is
GCF of Numerators i.e. for 197,406 is 1
LCM of denominators i.e. for 419,740 is 310060.
Thus, GCF of Fractions is 1/310060.Finally, GCF of Fractions for 197/419, 406/740 is 1/310060.