GCF of 1005/686, 6814/8766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1005/686, 6814/8766 i.e 1/3006738 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1005/686, 6814/8766.
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 1005/686,6814/8766?
Given fractions are 1005/686,6814/8766
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 1005/686,6814/8766, numerators are 1005,6814
Denominators are 686,8766
The GCF of 1005,6814 is 1 .
LCM of 686,8766 is 3006738.
The greatest common factor of 1005/686,6814/8766 = [GCF of 1005,6814]/[LCM of 686,8766]= 1/3006738
Therefore, the GCF of 1005/686,6814/8766 is 1/3006738.
To find the highest common factor of 1005,6814, we have to find the factors of both numbers and list the highest common factor.
The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005
The factors of 6814 are 1, 2, 3407, 6814
The HCF of 1005,6814 is 1.
Lets's calculate GCF of 1005,6814
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1005,6814 By Matching Biggest Common Factor Method
Now, list down the factors of 1005
:1,3,5,15,67,201,335,1005
Now, list down the factors of 6814
:1,2,3407,6814
Greatest Common Factor
We found the factors 1005,6814 . The biggest common factor number is the GCF number.
So the greatest common factor 1005,6814 is 1.
Lets's calculate LCM of 686,8766
| 2 | 686, 8766 |
| 343, 4383 |
∴ So the LCM of the given numbers is 2 x 343 x 4383 = 3006738
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3006738
Therefore, the GCF of Fractions 1005/686,6814/8766 is 1/3006738
Least Common Multiple of 686,8766 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 686,8766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(686,8766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(686,8766) x common factors =2 x 1 = 2
LCM(686,8766) = ( 686 × 8766 ) / 2
LCM(686,8766) = 6013476 / 2
LCM(686,8766) = 3006738
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1005/686, 6814/8766
1. What is the HCF of 1005,6814?
The HCF of 1005,6814 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 1005/686, 6814/8766?
Answer: GCF of Numerators as per given numbers 1005/686, 6814/8766 is
GCF of Numerators i.e. for 1005,6814 is 1
LCM of denominators i.e. for 686,8766 is 3006738.
Thus, GCF of Fractions is 1/3006738.Finally, GCF of Fractions for 1005/686, 6814/8766 is 1/3006738.