GCF of 2178/778, 8569/6686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2178/778, 8569/6686 i.e 11/2600854 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2178/778, 8569/6686.
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 2178/778,8569/6686?
Given fractions are 2178/778,8569/6686
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 2178/778,8569/6686, numerators are 2178,8569
Denominators are 778,6686
The GCF of 2178,8569 is 11 .
LCM of 778,6686 is 2600854.
The greatest common factor of 2178/778,8569/6686 = [GCF of 2178,8569]/[LCM of 778,6686]= 11/2600854
Therefore, the GCF of 2178/778,8569/6686 is 11/2600854.
To find the highest common factor of 2178,8569, we have to find the factors of both numbers and list the highest common factor.
The factors of 2178 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178
The factors of 8569 are 1, 11, 19, 41, 209, 451, 779, 8569
The HCF of 2178,8569 is 11.
Lets's calculate GCF of 2178,8569
| 11 | 2178, 8569 |
| 198, 779 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 2178,8569 By Matching Biggest Common Factor Method
Now, list down the factors of 2178
:1,2,3,6,9,11,18,22,33,66,99,121,198,242,363,726,1089,2178
Now, list down the factors of 8569
:1,11,19,41,209,451,779,8569
Greatest Common Factor
We found the factors 2178,8569 . The biggest common factor number is the GCF number.
So the greatest common factor 2178,8569 is 11.
Lets's calculate LCM of 778,6686
| 2 | 778, 6686 |
| 389, 3343 |
∴ So the LCM of the given numbers is 2 x 389 x 3343 = 2600854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/2600854
Therefore, the GCF of Fractions 2178/778,8569/6686 is 11/2600854
Least Common Multiple of 778,6686 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 778,6686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,6686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(778,6686) x common factors =2 x 1 = 2
LCM(778,6686) = ( 778 × 6686 ) / 2
LCM(778,6686) = 5201708 / 2
LCM(778,6686) = 2600854
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FAQs on GCF of Fractions of 2178/778, 8569/6686
1. What is the HCF of 2178,8569?
The HCF of 2178,8569 is 11
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 2178/778, 8569/6686?
Answer: GCF of Numerators as per given numbers 2178/778, 8569/6686 is
GCF of Numerators i.e. for 2178,8569 is 11
LCM of denominators i.e. for 778,6686 is 2600854.
Thus, GCF of Fractions is 11/2600854.Finally, GCF of Fractions for 2178/778, 8569/6686 is 11/2600854.