Use our free GCF of Fractions Calculator tool to compute the GCF of 289/338, 283/268 i.e 1/45292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/338, 283/268.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 289/338,283/268
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 289/338,283/268, numerators are 289,283
Denominators are 338,268
The GCF of 289,283 is 1 .
LCM of 338,268 is 45292.
The greatest common factor of 289/338,283/268 = [GCF of 289,283]/[LCM of 338,268]= 1/45292
Therefore, the GCF of 289/338,283/268 is 1/45292.
To find the highest common factor of 289,283, we have to find the factors of both numbers and list the highest common factor.
The factors of 289 are 1, 17, 289
The factors of 283 are 1, 283
The HCF of 289,283 is 1.
Lets's calculate GCF of 289,283
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 289
:1,17,289
Now, list down the factors of 283
:1,283
Greatest Common Factor
We found the factors 289,283 . The biggest common factor number is the GCF number.
So the greatest common factor 289,283 is 1.
Lets's calculate LCM of 338,268
2 | 338, 268 |
169, 134 |
∴ So the LCM of the given numbers is 2 x 169 x 134 = 45292
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45292
Therefore, the GCF of Fractions 289/338,283/268 is 1/45292
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 338,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(338,268) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(338,268) x common factors =2 x 1 = 2
LCM(338,268) = ( 338 × 268 ) / 2
LCM(338,268) = 90584 / 2
LCM(338,268) = 45292
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 289,283?
The HCF of 289,283 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 289/338, 283/268?
Answer: GCF of Numerators as per given numbers 289/338, 283/268 is
GCF of Numerators i.e. for 289,283 is 1
LCM of denominators i.e. for 338,268 is 45292.
Thus, GCF of Fractions is 1/45292.Finally, GCF of Fractions for 289/338, 283/268 is 1/45292.