Use our free GCF of Fractions Calculator tool to compute the GCF of 319/684, 897/249 i.e 1/56772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/684, 897/249.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 319/684,897/249
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 319/684,897/249, numerators are 319,897
Denominators are 684,249
The GCF of 319,897 is 1 .
LCM of 684,249 is 56772.
The greatest common factor of 319/684,897/249 = [GCF of 319,897]/[LCM of 684,249]= 1/56772
Therefore, the GCF of 319/684,897/249 is 1/56772.
To find the highest common factor of 319,897, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897
The HCF of 319,897 is 1.
Lets's calculate GCF of 319,897
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Greatest Common Factor
We found the factors 319,897 . The biggest common factor number is the GCF number.
So the greatest common factor 319,897 is 1.
Lets's calculate LCM of 684,249
3 | 684, 249 |
228, 83 |
∴ So the LCM of the given numbers is 3 x 228 x 83 = 56772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/56772
Therefore, the GCF of Fractions 319/684,897/249 is 1/56772
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 684,249 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,249) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(684,249) x common factors =3 x 1 = 3
LCM(684,249) = ( 684 × 249 ) / 3
LCM(684,249) = 170316 / 3
LCM(684,249) = 56772
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 319,897?
The HCF of 319,897 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 319/684, 897/249?
Answer: GCF of Numerators as per given numbers 319/684, 897/249 is
GCF of Numerators i.e. for 319,897 is 1
LCM of denominators i.e. for 684,249 is 56772.
Thus, GCF of Fractions is 1/56772.Finally, GCF of Fractions for 319/684, 897/249 is 1/56772.