GCF of 5705/260, 6867/8314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5705/260, 6867/8314 i.e 7/1080820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5705/260, 6867/8314.
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 5705/260,6867/8314?
Given fractions are 5705/260,6867/8314
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 5705/260,6867/8314, numerators are 5705,6867
Denominators are 260,8314
The GCF of 5705,6867 is 7 .
LCM of 260,8314 is 1080820.
The greatest common factor of 5705/260,6867/8314 = [GCF of 5705,6867]/[LCM of 260,8314]= 7/1080820
Therefore, the GCF of 5705/260,6867/8314 is 7/1080820.
To find the highest common factor of 5705,6867, we have to find the factors of both numbers and list the highest common factor.
The factors of 5705 are 1, 5, 7, 35, 163, 815, 1141, 5705
The factors of 6867 are 1, 3, 7, 9, 21, 63, 109, 327, 763, 981, 2289, 6867
The HCF of 5705,6867 is 7.
Lets's calculate GCF of 5705,6867
| 7 | 5705, 6867 |
| 815, 981 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 5705,6867 By Matching Biggest Common Factor Method
Now, list down the factors of 5705
:1,5,7,35,163,815,1141,5705
Now, list down the factors of 6867
:1,3,7,9,21,63,109,327,763,981,2289,6867
Greatest Common Factor
We found the factors 5705,6867 . The biggest common factor number is the GCF number.
So the greatest common factor 5705,6867 is 7.
Lets's calculate LCM of 260,8314
| 2 | 260, 8314 |
| 130, 4157 |
∴ So the LCM of the given numbers is 2 x 130 x 4157 = 1080820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/1080820
Therefore, the GCF of Fractions 5705/260,6867/8314 is 7/1080820
Least Common Multiple of 260,8314 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 260,8314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,8314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(260,8314) x common factors =2 x 1 = 2
LCM(260,8314) = ( 260 × 8314 ) / 2
LCM(260,8314) = 2161640 / 2
LCM(260,8314) = 1080820
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 5705/260, 6867/8314
1. What is the HCF of 5705,6867?
The HCF of 5705,6867 is 7
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 5705/260, 6867/8314?
Answer: GCF of Numerators as per given numbers 5705/260, 6867/8314 is
GCF of Numerators i.e. for 5705,6867 is 7
LCM of denominators i.e. for 260,8314 is 1080820.
Thus, GCF of Fractions is 7/1080820.Finally, GCF of Fractions for 5705/260, 6867/8314 is 7/1080820.