Use our free GCF of Fractions Calculator tool to compute the GCF of 519/504, 538/405 i.e 1/22680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 519/504, 538/405.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 519/504,538/405
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 519/504,538/405, numerators are 519,538
Denominators are 504,405
The GCF of 519,538 is 1 .
LCM of 504,405 is 22680.
The greatest common factor of 519/504,538/405 = [GCF of 519,538]/[LCM of 504,405]= 1/22680
Therefore, the GCF of 519/504,538/405 is 1/22680.
To find the highest common factor of 519,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 519 are 1, 3, 173, 519
The factors of 538 are 1, 2, 269, 538
The HCF of 519,538 is 1.
Lets's calculate GCF of 519,538
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 519
:1,3,173,519
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 519,538 . The biggest common factor number is the GCF number.
So the greatest common factor 519,538 is 1.
Lets's calculate LCM of 504,405
3 | 504, 405 |
3 | 168, 135 |
56, 45 |
∴ So the LCM of the given numbers is 3 x 3 x 56 x 45 = 22680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/22680
Therefore, the GCF of Fractions 519/504,538/405 is 1/22680
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 504,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(504,405) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(504,405) x common factors =9 x 1 = 9
LCM(504,405) = ( 504 × 405 ) / 9
LCM(504,405) = 204120 / 9
LCM(504,405) = 22680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 519,538?
The HCF of 519,538 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 519/504, 538/405?
Answer: GCF of Numerators as per given numbers 519/504, 538/405 is
GCF of Numerators i.e. for 519,538 is 1
LCM of denominators i.e. for 504,405 is 22680.
Thus, GCF of Fractions is 1/22680.Finally, GCF of Fractions for 519/504, 538/405 is 1/22680.