Use our free GCF of Fractions Calculator tool to compute the GCF of 589/249, 195/978 i.e 1/81174 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/249, 195/978.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 589/249,195/978
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 589/249,195/978, numerators are 589,195
Denominators are 249,978
The GCF of 589,195 is 1 .
LCM of 249,978 is 81174.
The greatest common factor of 589/249,195/978 = [GCF of 589,195]/[LCM of 249,978]= 1/81174
Therefore, the GCF of 589/249,195/978 is 1/81174.
To find the highest common factor of 589,195, we have to find the factors of both numbers and list the highest common factor.
The factors of 589 are 1, 19, 31, 589
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195
The HCF of 589,195 is 1.
Lets's calculate GCF of 589,195
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 195
:1,3,5,13,15,39,65,195
Greatest Common Factor
We found the factors 589,195 . The biggest common factor number is the GCF number.
So the greatest common factor 589,195 is 1.
Lets's calculate LCM of 249,978
3 | 249, 978 |
83, 326 |
∴ So the LCM of the given numbers is 3 x 83 x 326 = 81174
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/81174
Therefore, the GCF of Fractions 589/249,195/978 is 1/81174
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 249,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(249,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(249,978) x common factors =3 x 1 = 3
LCM(249,978) = ( 249 × 978 ) / 3
LCM(249,978) = 243522 / 3
LCM(249,978) = 81174
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 589,195?
The HCF of 589,195 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 589/249, 195/978?
Answer: GCF of Numerators as per given numbers 589/249, 195/978 is
GCF of Numerators i.e. for 589,195 is 1
LCM of denominators i.e. for 249,978 is 81174.
Thus, GCF of Fractions is 1/81174.Finally, GCF of Fractions for 589/249, 195/978 is 1/81174.