Use our free GCF of Fractions Calculator tool to compute the GCF of 494/414, 359/729 i.e 1/33534 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/414, 359/729.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 494/414,359/729
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 494/414,359/729, numerators are 494,359
Denominators are 414,729
The GCF of 494,359 is 1 .
LCM of 414,729 is 33534.
The greatest common factor of 494/414,359/729 = [GCF of 494,359]/[LCM of 414,729]= 1/33534
Therefore, the GCF of 494/414,359/729 is 1/33534.
To find the highest common factor of 494,359, 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 359 are 1, 359
The HCF of 494,359 is 1.
Lets's calculate GCF of 494,359
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 494
:1,2,13,19,26,38,247,494
Now, list down the factors of 359
:1,359
Greatest Common Factor
We found the factors 494,359 . The biggest common factor number is the GCF number.
So the greatest common factor 494,359 is 1.
Lets's calculate LCM of 414,729
3 | 414, 729 |
3 | 138, 243 |
46, 81 |
∴ So the LCM of the given numbers is 3 x 3 x 46 x 81 = 33534
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33534
Therefore, the GCF of Fractions 494/414,359/729 is 1/33534
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 414,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,729) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(414,729) x common factors =9 x 1 = 9
LCM(414,729) = ( 414 × 729 ) / 9
LCM(414,729) = 301806 / 9
LCM(414,729) = 33534
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 494,359?
The HCF of 494,359 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 494/414, 359/729?
Answer: GCF of Numerators as per given numbers 494/414, 359/729 is
GCF of Numerators i.e. for 494,359 is 1
LCM of denominators i.e. for 414,729 is 33534.
Thus, GCF of Fractions is 1/33534.Finally, GCF of Fractions for 494/414, 359/729 is 1/33534.