Use our free GCF of Fractions Calculator tool to compute the GCF of 413/338, 410/798 i.e 1/134862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 413/338, 410/798.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 413/338,410/798
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 413/338,410/798, numerators are 413,410
Denominators are 338,798
The GCF of 413,410 is 1 .
LCM of 338,798 is 134862.
The greatest common factor of 413/338,410/798 = [GCF of 413,410]/[LCM of 338,798]= 1/134862
Therefore, the GCF of 413/338,410/798 is 1/134862.
To find the highest common factor of 413,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 413 are 1, 7, 59, 413
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 413,410 is 1.
Lets's calculate GCF of 413,410
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 413
:1,7,59,413
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 413,410 . The biggest common factor number is the GCF number.
So the greatest common factor 413,410 is 1.
Lets's calculate LCM of 338,798
2 | 338, 798 |
169, 399 |
∴ So the LCM of the given numbers is 2 x 169 x 399 = 134862
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/134862
Therefore, the GCF of Fractions 413/338,410/798 is 1/134862
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 338,798 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(338,798) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(338,798) x common factors =2 x 1 = 2
LCM(338,798) = ( 338 × 798 ) / 2
LCM(338,798) = 269724 / 2
LCM(338,798) = 134862
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 413,410?
The HCF of 413,410 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 413/338, 410/798?
Answer: GCF of Numerators as per given numbers 413/338, 410/798 is
GCF of Numerators i.e. for 413,410 is 1
LCM of denominators i.e. for 338,798 is 134862.
Thus, GCF of Fractions is 1/134862.Finally, GCF of Fractions for 413/338, 410/798 is 1/134862.