GCF of 115/208, 8289/580
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 115/208, 8289/580 i.e 1/30160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 115/208, 8289/580.
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 115/208,8289/580?
Given fractions are 115/208,8289/580
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 115/208,8289/580, numerators are 115,8289
Denominators are 208,580
The GCF of 115,8289 is 1 .
LCM of 208,580 is 30160.
The greatest common factor of 115/208,8289/580 = [GCF of 115,8289]/[LCM of 208,580]= 1/30160
Therefore, the GCF of 115/208,8289/580 is 1/30160.
To find the highest common factor of 115,8289, we have to find the factors of both numbers and list the highest common factor.
The factors of 115 are 1, 5, 23, 115
The factors of 8289 are 1, 3, 9, 27, 307, 921, 2763, 8289
The HCF of 115,8289 is 1.
Lets's calculate GCF of 115,8289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 115,8289 By Matching Biggest Common Factor Method
Now, list down the factors of 115
:1,5,23,115
Now, list down the factors of 8289
:1,3,9,27,307,921,2763,8289
Greatest Common Factor
We found the factors 115,8289 . The biggest common factor number is the GCF number.
So the greatest common factor 115,8289 is 1.
Lets's calculate LCM of 208,580
| 2 | 208, 580 |
| 2 | 104, 290 |
| 52, 145 |
∴ So the LCM of the given numbers is 2 x 2 x 52 x 145 = 30160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30160
Therefore, the GCF of Fractions 115/208,8289/580 is 1/30160
Least Common Multiple of 208,580 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 208,580 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,580) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(208,580) x common factors =4 x 1 = 4
LCM(208,580) = ( 208 × 580 ) / 4
LCM(208,580) = 120640 / 4
LCM(208,580) = 30160
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FAQs on GCF of Fractions of 115/208, 8289/580
1. What is the HCF of 115,8289?
The HCF of 115,8289 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 115/208, 8289/580?
Answer: GCF of Numerators as per given numbers 115/208, 8289/580 is
GCF of Numerators i.e. for 115,8289 is 1
LCM of denominators i.e. for 208,580 is 30160.
Thus, GCF of Fractions is 1/30160.Finally, GCF of Fractions for 115/208, 8289/580 is 1/30160.