Use our free GCF of Fractions Calculator tool to compute the GCF of 514/586, 584/241 i.e 2/141226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/586, 584/241.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 514/586,584/241
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 514/586,584/241, numerators are 514,584
Denominators are 586,241
The GCF of 514,584 is 2 .
LCM of 586,241 is 141226.
The greatest common factor of 514/586,584/241 = [GCF of 514,584]/[LCM of 586,241]= 2/141226
Therefore, the GCF of 514/586,584/241 is 2/141226.
To find the highest common factor of 514,584, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The HCF of 514,584 is 2.
Lets's calculate GCF of 514,584
2 | 514, 584 |
257, 292 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Greatest Common Factor
We found the factors 514,584 . The biggest common factor number is the GCF number.
So the greatest common factor 514,584 is 2.
Lets's calculate LCM of 586,241
Given numbers has no common factors except 1. So, there LCM is their product i.e 141226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/141226
Therefore, the GCF of Fractions 514/586,584/241 is 2/141226
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 586,241 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,241) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(586,241) x common factors =1 x 1 = 1
LCM(586,241) = ( 586 × 241 ) / 1
LCM(586,241) = 141226 / 1
LCM(586,241) = 141226
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 514,584?
The HCF of 514,584 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 514/586, 584/241?
Answer: GCF of Numerators as per given numbers 514/586, 584/241 is
GCF of Numerators i.e. for 514,584 is 2
LCM of denominators i.e. for 586,241 is 141226.
Thus, GCF of Fractions is 2/141226.Finally, GCF of Fractions for 514/586, 584/241 is 2/141226.