GCF of 2085/646, 1809/5301
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2085/646, 1809/5301 i.e 3/180234 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2085/646, 1809/5301.
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 2085/646,1809/5301?
Given fractions are 2085/646,1809/5301
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 2085/646,1809/5301, numerators are 2085,1809
Denominators are 646,5301
The GCF of 2085,1809 is 3 .
LCM of 646,5301 is 180234.
The greatest common factor of 2085/646,1809/5301 = [GCF of 2085,1809]/[LCM of 646,5301]= 3/180234
Therefore, the GCF of 2085/646,1809/5301 is 3/180234.
To find the highest common factor of 2085,1809, we have to find the factors of both numbers and list the highest common factor.
The factors of 2085 are 1, 3, 5, 15, 139, 417, 695, 2085
The factors of 1809 are 1, 3, 9, 27, 67, 201, 603, 1809
The HCF of 2085,1809 is 3.
Lets's calculate GCF of 2085,1809
| 3 | 2085, 1809 |
| 695, 603 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2085,1809 By Matching Biggest Common Factor Method
Now, list down the factors of 2085
:1,3,5,15,139,417,695,2085
Now, list down the factors of 1809
:1,3,9,27,67,201,603,1809
Greatest Common Factor
We found the factors 2085,1809 . The biggest common factor number is the GCF number.
So the greatest common factor 2085,1809 is 3.
Lets's calculate LCM of 646,5301
| 19 | 646, 5301 |
| 34, 279 |
∴ So the LCM of the given numbers is 19 x 34 x 279 = 180234
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/180234
Therefore, the GCF of Fractions 2085/646,1809/5301 is 3/180234
Least Common Multiple of 646,5301 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 646,5301 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(646,5301) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(646,5301) x common factors =19 x 1 = 19
LCM(646,5301) = ( 646 × 5301 ) / 19
LCM(646,5301) = 3424446 / 19
LCM(646,5301) = 180234
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FAQs on GCF of Fractions of 2085/646, 1809/5301
1. What is the HCF of 2085,1809?
The HCF of 2085,1809 is 3
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 2085/646, 1809/5301?
Answer: GCF of Numerators as per given numbers 2085/646, 1809/5301 is
GCF of Numerators i.e. for 2085,1809 is 3
LCM of denominators i.e. for 646,5301 is 180234.
Thus, GCF of Fractions is 3/180234.Finally, GCF of Fractions for 2085/646, 1809/5301 is 3/180234.