Use our free GCF of Fractions Calculator tool to compute the GCF of 728/685, 313/320 i.e 1/43840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/685, 313/320.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 728/685,313/320
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 728/685,313/320, numerators are 728,313
Denominators are 685,320
The GCF of 728,313 is 1 .
LCM of 685,320 is 43840.
The greatest common factor of 728/685,313/320 = [GCF of 728,313]/[LCM of 685,320]= 1/43840
Therefore, the GCF of 728/685,313/320 is 1/43840.
To find the highest common factor of 728,313, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 313 are 1, 313
The HCF of 728,313 is 1.
Lets's calculate GCF of 728,313
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 313
:1,313
Greatest Common Factor
We found the factors 728,313 . The biggest common factor number is the GCF number.
So the greatest common factor 728,313 is 1.
Lets's calculate LCM of 685,320
5 | 685, 320 |
137, 64 |
∴ So the LCM of the given numbers is 5 x 137 x 64 = 43840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43840
Therefore, the GCF of Fractions 728/685,313/320 is 1/43840
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 685,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(685,320) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(685,320) x common factors =5 x 1 = 5
LCM(685,320) = ( 685 × 320 ) / 5
LCM(685,320) = 219200 / 5
LCM(685,320) = 43840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 728,313?
The HCF of 728,313 is 1
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 728/685, 313/320?
Answer: GCF of Numerators as per given numbers 728/685, 313/320 is
GCF of Numerators i.e. for 728,313 is 1
LCM of denominators i.e. for 685,320 is 43840.
Thus, GCF of Fractions is 1/43840.Finally, GCF of Fractions for 728/685, 313/320 is 1/43840.