Use our free GCF of Fractions Calculator tool to compute the GCF of 181/298, 377/214 i.e 1/31886 easily. The following is the detailed procedure to determine the greatest common factor of fractions 181/298, 377/214.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 181/298,377/214
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 181/298,377/214, numerators are 181,377
Denominators are 298,214
The GCF of 181,377 is 1 .
LCM of 298,214 is 31886.
The greatest common factor of 181/298,377/214 = [GCF of 181,377]/[LCM of 298,214]= 1/31886
Therefore, the GCF of 181/298,377/214 is 1/31886.
To find the highest common factor of 181,377, we have to find the factors of both numbers and list the highest common factor.
The factors of 181 are 1, 181
The factors of 377 are 1, 13, 29, 377
The HCF of 181,377 is 1.
Lets's calculate GCF of 181,377
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 181
:1,181
Now, list down the factors of 377
:1,13,29,377
Greatest Common Factor
We found the factors 181,377 . The biggest common factor number is the GCF number.
So the greatest common factor 181,377 is 1.
Lets's calculate LCM of 298,214
2 | 298, 214 |
149, 107 |
∴ So the LCM of the given numbers is 2 x 149 x 107 = 31886
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31886
Therefore, the GCF of Fractions 181/298,377/214 is 1/31886
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 298,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(298,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(298,214) x common factors =2 x 1 = 2
LCM(298,214) = ( 298 × 214 ) / 2
LCM(298,214) = 63772 / 2
LCM(298,214) = 31886
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 181,377?
The HCF of 181,377 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 181/298, 377/214?
Answer: GCF of Numerators as per given numbers 181/298, 377/214 is
GCF of Numerators i.e. for 181,377 is 1
LCM of denominators i.e. for 298,214 is 31886.
Thus, GCF of Fractions is 1/31886.Finally, GCF of Fractions for 181/298, 377/214 is 1/31886.