Use our free GCF of Fractions Calculator tool to compute the GCF of 640/978, 320/806 i.e 320/394134 easily. The following is the detailed procedure to determine the greatest common factor of fractions 640/978, 320/806.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 640/978,320/806
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 640/978,320/806, numerators are 640,320
Denominators are 978,806
The GCF of 640,320 is 320 .
LCM of 978,806 is 394134.
The greatest common factor of 640/978,320/806 = [GCF of 640,320]/[LCM of 978,806]= 320/394134
Therefore, the GCF of 640/978,320/806 is 320/394134.
To find the highest common factor of 640,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 640,320 is 320.
Lets's calculate GCF of 640,320
2 | 640, 320 |
2 | 320, 160 |
2 | 80, 160 |
2 | 40, 80 |
2 | 20, 40 |
2 | 10, 20 |
5 | 5, 10 |
1, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 5 = 320
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 640,320 . The biggest common factor number is the GCF number.
So the greatest common factor 640,320 is 320.
Lets's calculate LCM of 978,806
2 | 978, 806 |
489, 403 |
∴ So the LCM of the given numbers is 2 x 489 x 403 = 394134
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 320/394134
Therefore, the GCF of Fractions 640/978,320/806 is 320/394134
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 978,806 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,806) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(978,806) x common factors =2 x 1 = 2
LCM(978,806) = ( 978 × 806 ) / 2
LCM(978,806) = 788268 / 2
LCM(978,806) = 394134
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 640,320?
The HCF of 640,320 is 320
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 640/978, 320/806?
Answer: GCF of Numerators as per given numbers 640/978, 320/806 is
GCF of Numerators i.e. for 640,320 is 320
LCM of denominators i.e. for 978,806 is 394134.
Thus, GCF of Fractions is 320/394134.Finally, GCF of Fractions for 640/978, 320/806 is 320/394134.