Use our free GCF of Fractions Calculator tool to compute the GCF of 592/340, 518/289 i.e 74/5780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/340, 518/289.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 592/340,518/289
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 592/340,518/289, numerators are 592,518
Denominators are 340,289
The GCF of 592,518 is 74 .
LCM of 340,289 is 5780.
The greatest common factor of 592/340,518/289 = [GCF of 592,518]/[LCM of 340,289]= 74/5780
Therefore, the GCF of 592/340,518/289 is 74/5780.
To find the highest common factor of 592,518, we have to find the factors of both numbers and list the highest common factor.
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518
The HCF of 592,518 is 74.
Lets's calculate GCF of 592,518
2 | 592, 518 |
37 | 296, 259 |
8, 7 |
∴ So the GCF of the given numbers is 2 x 37 = 74
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Now, list down the factors of 518
:1,2,7,14,37,74,259,518
Greatest Common Factor
We found the factors 592,518 . The biggest common factor number is the GCF number.
So the greatest common factor 592,518 is 74.
Lets's calculate LCM of 340,289
17 | 340, 289 |
20, 17 |
∴ So the LCM of the given numbers is 17 x 20 x 17 = 5780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 74/5780
Therefore, the GCF of Fractions 592/340,518/289 is 74/5780
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 340,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,289) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(340,289) x common factors =17 x 1 = 17
LCM(340,289) = ( 340 × 289 ) / 17
LCM(340,289) = 98260 / 17
LCM(340,289) = 5780
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 592,518?
The HCF of 592,518 is 74
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 592/340, 518/289?
Answer: GCF of Numerators as per given numbers 592/340, 518/289 is
GCF of Numerators i.e. for 592,518 is 74
LCM of denominators i.e. for 340,289 is 5780.
Thus, GCF of Fractions is 74/5780.Finally, GCF of Fractions for 592/340, 518/289 is 74/5780.