GCF of 6774/678, 8109/2836
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6774/678, 8109/2836 i.e 3/961404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6774/678, 8109/2836.
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 6774/678,8109/2836?
Given fractions are 6774/678,8109/2836
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 6774/678,8109/2836, numerators are 6774,8109
Denominators are 678,2836
The GCF of 6774,8109 is 3 .
LCM of 678,2836 is 961404.
The greatest common factor of 6774/678,8109/2836 = [GCF of 6774,8109]/[LCM of 678,2836]= 3/961404
Therefore, the GCF of 6774/678,8109/2836 is 3/961404.
To find the highest common factor of 6774,8109, we have to find the factors of both numbers and list the highest common factor.
The factors of 6774 are 1, 2, 3, 6, 1129, 2258, 3387, 6774
The factors of 8109 are 1, 3, 9, 17, 51, 53, 153, 159, 477, 901, 2703, 8109
The HCF of 6774,8109 is 3.
Lets's calculate GCF of 6774,8109
| 3 | 6774, 8109 |
| 2258, 2703 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 6774,8109 By Matching Biggest Common Factor Method
Now, list down the factors of 6774
:1,2,3,6,1129,2258,3387,6774
Now, list down the factors of 8109
:1,3,9,17,51,53,153,159,477,901,2703,8109
Greatest Common Factor
We found the factors 6774,8109 . The biggest common factor number is the GCF number.
So the greatest common factor 6774,8109 is 3.
Lets's calculate LCM of 678,2836
| 2 | 678, 2836 |
| 339, 1418 |
∴ So the LCM of the given numbers is 2 x 339 x 1418 = 961404
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/961404
Therefore, the GCF of Fractions 6774/678,8109/2836 is 3/961404
Least Common Multiple of 678,2836 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 678,2836 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,2836) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,2836) x common factors =2 x 1 = 2
LCM(678,2836) = ( 678 × 2836 ) / 2
LCM(678,2836) = 1922808 / 2
LCM(678,2836) = 961404
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FAQs on GCF of Fractions of 6774/678, 8109/2836
1. What is the HCF of 6774,8109?
The HCF of 6774,8109 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 6774/678, 8109/2836?
Answer: GCF of Numerators as per given numbers 6774/678, 8109/2836 is
GCF of Numerators i.e. for 6774,8109 is 3
LCM of denominators i.e. for 678,2836 is 961404.
Thus, GCF of Fractions is 3/961404.Finally, GCF of Fractions for 6774/678, 8109/2836 is 3/961404.