Use our free GCF of Fractions Calculator tool to compute the GCF of 721/313, 378/986 i.e 7/308618 easily. The following is the detailed procedure to determine the greatest common factor of fractions 721/313, 378/986.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 721/313,378/986
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 721/313,378/986, numerators are 721,378
Denominators are 313,986
The GCF of 721,378 is 7 .
LCM of 313,986 is 308618.
The greatest common factor of 721/313,378/986 = [GCF of 721,378]/[LCM of 313,986]= 7/308618
Therefore, the GCF of 721/313,378/986 is 7/308618.
To find the highest common factor of 721,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 721 are 1, 7, 103, 721
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 721,378 is 7.
Lets's calculate GCF of 721,378
7 | 721, 378 |
103, 54 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 721
:1,7,103,721
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 721,378 . The biggest common factor number is the GCF number.
So the greatest common factor 721,378 is 7.
Lets's calculate LCM of 313,986
Given numbers has no common factors except 1. So, there LCM is their product i.e 308618
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/308618
Therefore, the GCF of Fractions 721/313,378/986 is 7/308618
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 313,986 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(313,986) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(313,986) x common factors =1 x 1 = 1
LCM(313,986) = ( 313 × 986 ) / 1
LCM(313,986) = 308618 / 1
LCM(313,986) = 308618
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 721,378?
The HCF of 721,378 is 7
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 721/313, 378/986?
Answer: GCF of Numerators as per given numbers 721/313, 378/986 is
GCF of Numerators i.e. for 721,378 is 7
LCM of denominators i.e. for 313,986 is 308618.
Thus, GCF of Fractions is 7/308618.Finally, GCF of Fractions for 721/313, 378/986 is 7/308618.