Use our free GCF of Fractions Calculator tool to compute the GCF of 181/78, 698/209 i.e 1/16302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 181/78, 698/209.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 181/78,698/209
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 181/78,698/209, numerators are 181,698
Denominators are 78,209
The GCF of 181,698 is 1 .
LCM of 78,209 is 16302.
The greatest common factor of 181/78,698/209 = [GCF of 181,698]/[LCM of 78,209]= 1/16302
Therefore, the GCF of 181/78,698/209 is 1/16302.
To find the highest common factor of 181,698, 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 698 are 1, 2, 349, 698
The HCF of 181,698 is 1.
Lets's calculate GCF of 181,698
∴ 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 698
:1,2,349,698
Greatest Common Factor
We found the factors 181,698 . The biggest common factor number is the GCF number.
So the greatest common factor 181,698 is 1.
Lets's calculate LCM of 78,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 16302
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16302
Therefore, the GCF of Fractions 181/78,698/209 is 1/16302
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 78,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(78,209) x common factors =1 x 1 = 1
LCM(78,209) = ( 78 × 209 ) / 1
LCM(78,209) = 16302 / 1
LCM(78,209) = 16302
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 181,698?
The HCF of 181,698 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 181/78, 698/209?
Answer: GCF of Numerators as per given numbers 181/78, 698/209 is
GCF of Numerators i.e. for 181,698 is 1
LCM of denominators i.e. for 78,209 is 16302.
Thus, GCF of Fractions is 1/16302.Finally, GCF of Fractions for 181/78, 698/209 is 1/16302.