Use our free GCF of Fractions Calculator tool to compute the GCF of 306/721, 663/419 i.e 51/302099 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/721, 663/419.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 306/721,663/419
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 306/721,663/419, numerators are 306,663
Denominators are 721,419
The GCF of 306,663 is 51 .
LCM of 721,419 is 302099.
The greatest common factor of 306/721,663/419 = [GCF of 306,663]/[LCM of 721,419]= 51/302099
Therefore, the GCF of 306/721,663/419 is 51/302099.
To find the highest common factor of 306,663, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The HCF of 306,663 is 51.
Lets's calculate GCF of 306,663
3 | 306, 663 |
17 | 102, 221 |
6, 13 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
Greatest Common Factor
We found the factors 306,663 . The biggest common factor number is the GCF number.
So the greatest common factor 306,663 is 51.
Lets's calculate LCM of 721,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 302099
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/302099
Therefore, the GCF of Fractions 306/721,663/419 is 51/302099
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 721,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(721,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(721,419) x common factors =1 x 1 = 1
LCM(721,419) = ( 721 × 419 ) / 1
LCM(721,419) = 302099 / 1
LCM(721,419) = 302099
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 306,663?
The HCF of 306,663 is 51
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 306/721, 663/419?
Answer: GCF of Numerators as per given numbers 306/721, 663/419 is
GCF of Numerators i.e. for 306,663 is 51
LCM of denominators i.e. for 721,419 is 302099.
Thus, GCF of Fractions is 51/302099.Finally, GCF of Fractions for 306/721, 663/419 is 51/302099.