GCF of 589/322, 200/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 589/322, 200/108 i.e 1/17388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/322, 200/108.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 589/322,200/108?
Given fractions are 589/322,200/108
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 589/322,200/108, numerators are 589,200
Denominators are 322,108
The GCF of 589,200 is 1 .
LCM of 322,108 is 17388.
The greatest common factor of 589/322,200/108 = [GCF of 589,200]/[LCM of 322,108]= 1/17388
Therefore, the GCF of 589/322,200/108 is 1/17388.
To find the highest common factor of 589,200, we have to find the factors of both numbers and list the highest common factor.
The factors of 589 are 1, 19, 31, 589
The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
The HCF of 589,200 is 1.
Lets's calculate GCF of 589,200
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 589,200 By Matching Biggest Common Factor Method
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 200
:1,2,4,5,8,10,20,25,40,50,100,200
Greatest Common Factor
We found the factors 589,200 . The biggest common factor number is the GCF number.
So the greatest common factor 589,200 is 1.
Lets's calculate LCM of 322,108
| 2 | 322, 108 |
| 161, 54 |
∴ So the LCM of the given numbers is 2 x 161 x 54 = 17388
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17388
Therefore, the GCF of Fractions 589/322,200/108 is 1/17388
Least Common Multiple of 322,108 with GCF Formula
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 322,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(322,108) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(322,108) x common factors =2 x 1 = 2
LCM(322,108) = ( 322 × 108 ) / 2
LCM(322,108) = 34776 / 2
LCM(322,108) = 17388
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 589/322, 200/108
1. What is the HCF of 589,200?
The HCF of 589,200 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 589/322, 200/108?
Answer: GCF of Numerators as per given numbers 589/322, 200/108 is
GCF of Numerators i.e. for 589,200 is 1
LCM of denominators i.e. for 322,108 is 17388.
Thus, GCF of Fractions is 1/17388.Finally, GCF of Fractions for 589/322, 200/108 is 1/17388.