Use our free GCF of Fractions Calculator tool to compute the GCF of 494/413, 538/262 i.e 2/108206 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/413, 538/262.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 494/413,538/262
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 494/413,538/262, numerators are 494,538
Denominators are 413,262
The GCF of 494,538 is 2 .
LCM of 413,262 is 108206.
The greatest common factor of 494/413,538/262 = [GCF of 494,538]/[LCM of 413,262]= 2/108206
Therefore, the GCF of 494/413,538/262 is 2/108206.
To find the highest common factor of 494,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494
The factors of 538 are 1, 2, 269, 538
The HCF of 494,538 is 2.
Lets's calculate GCF of 494,538
2 | 494, 538 |
247, 269 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 494
:1,2,13,19,26,38,247,494
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 494,538 . The biggest common factor number is the GCF number.
So the greatest common factor 494,538 is 2.
Lets's calculate LCM of 413,262
Given numbers has no common factors except 1. So, there LCM is their product i.e 108206
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/108206
Therefore, the GCF of Fractions 494/413,538/262 is 2/108206
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 413,262 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,262) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,262) x common factors =1 x 1 = 1
LCM(413,262) = ( 413 × 262 ) / 1
LCM(413,262) = 108206 / 1
LCM(413,262) = 108206
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 494,538?
The HCF of 494,538 is 2
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 494/413, 538/262?
Answer: GCF of Numerators as per given numbers 494/413, 538/262 is
GCF of Numerators i.e. for 494,538 is 2
LCM of denominators i.e. for 413,262 is 108206.
Thus, GCF of Fractions is 2/108206.Finally, GCF of Fractions for 494/413, 538/262 is 2/108206.