Use our free GCF of Fractions Calculator tool to compute the GCF of 588/418, 306/763 i.e 6/318934 easily. The following is the detailed procedure to determine the greatest common factor of fractions 588/418, 306/763.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 588/418,306/763
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 588/418,306/763, numerators are 588,306
Denominators are 418,763
The GCF of 588,306 is 6 .
LCM of 418,763 is 318934.
The greatest common factor of 588/418,306/763 = [GCF of 588,306]/[LCM of 418,763]= 6/318934
Therefore, the GCF of 588/418,306/763 is 6/318934.
To find the highest common factor of 588,306, we have to find the factors of both numbers and list the highest common factor.
The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The HCF of 588,306 is 6.
Lets's calculate GCF of 588,306
2 | 588, 306 |
3 | 294, 153 |
98, 51 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 588
:1,2,3,4,6,7,12,14,21,28,42,49,84,98,147,196,294,588
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Greatest Common Factor
We found the factors 588,306 . The biggest common factor number is the GCF number.
So the greatest common factor 588,306 is 6.
Lets's calculate LCM of 418,763
Given numbers has no common factors except 1. So, there LCM is their product i.e 318934
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/318934
Therefore, the GCF of Fractions 588/418,306/763 is 6/318934
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 418,763 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(418,763) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(418,763) x common factors =1 x 1 = 1
LCM(418,763) = ( 418 × 763 ) / 1
LCM(418,763) = 318934 / 1
LCM(418,763) = 318934
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 588,306?
The HCF of 588,306 is 6
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 588/418, 306/763?
Answer: GCF of Numerators as per given numbers 588/418, 306/763 is
GCF of Numerators i.e. for 588,306 is 6
LCM of denominators i.e. for 418,763 is 318934.
Thus, GCF of Fractions is 6/318934.Finally, GCF of Fractions for 588/418, 306/763 is 6/318934.