GCF of 2109/721, 5287/1757
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2109/721, 5287/1757 i.e 1/180971 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2109/721, 5287/1757.
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 2109/721,5287/1757?
Given fractions are 2109/721,5287/1757
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 2109/721,5287/1757, numerators are 2109,5287
Denominators are 721,1757
The GCF of 2109,5287 is 1 .
LCM of 721,1757 is 180971.
The greatest common factor of 2109/721,5287/1757 = [GCF of 2109,5287]/[LCM of 721,1757]= 1/180971
Therefore, the GCF of 2109/721,5287/1757 is 1/180971.
To find the highest common factor of 2109,5287, we have to find the factors of both numbers and list the highest common factor.
The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109
The factors of 5287 are 1, 17, 311, 5287
The HCF of 2109,5287 is 1.
Lets's calculate GCF of 2109,5287
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2109,5287 By Matching Biggest Common Factor Method
Now, list down the factors of 2109
:1,3,19,37,57,111,703,2109
Now, list down the factors of 5287
:1,17,311,5287
Greatest Common Factor
We found the factors 2109,5287 . The biggest common factor number is the GCF number.
So the greatest common factor 2109,5287 is 1.
Lets's calculate LCM of 721,1757
| 7 | 721, 1757 |
| 103, 251 |
∴ So the LCM of the given numbers is 7 x 103 x 251 = 180971
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/180971
Therefore, the GCF of Fractions 2109/721,5287/1757 is 1/180971
Least Common Multiple of 721,1757 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 721,1757 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(721,1757) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(721,1757) x common factors =7 x 1 = 7
LCM(721,1757) = ( 721 × 1757 ) / 7
LCM(721,1757) = 1266797 / 7
LCM(721,1757) = 180971
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 2109/721, 5287/1757
1. What is the HCF of 2109,5287?
The HCF of 2109,5287 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 2109/721, 5287/1757?
Answer: GCF of Numerators as per given numbers 2109/721, 5287/1757 is
GCF of Numerators i.e. for 2109,5287 is 1
LCM of denominators i.e. for 721,1757 is 180971.
Thus, GCF of Fractions is 1/180971.Finally, GCF of Fractions for 2109/721, 5287/1757 is 1/180971.