GCF of 1746/205, 8684/7653
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1746/205, 8684/7653 i.e 2/1568865 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1746/205, 8684/7653.
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 1746/205,8684/7653?
Given fractions are 1746/205,8684/7653
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 1746/205,8684/7653, numerators are 1746,8684
Denominators are 205,7653
The GCF of 1746,8684 is 2 .
LCM of 205,7653 is 1568865.
The greatest common factor of 1746/205,8684/7653 = [GCF of 1746,8684]/[LCM of 205,7653]= 2/1568865
Therefore, the GCF of 1746/205,8684/7653 is 2/1568865.
To find the highest common factor of 1746,8684, we have to find the factors of both numbers and list the highest common factor.
The factors of 1746 are 1, 2, 3, 6, 9, 18, 97, 194, 291, 582, 873, 1746
The factors of 8684 are 1, 2, 4, 13, 26, 52, 167, 334, 668, 2171, 4342, 8684
The HCF of 1746,8684 is 2.
Lets's calculate GCF of 1746,8684
| 2 | 1746, 8684 |
| 873, 4342 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1746,8684 By Matching Biggest Common Factor Method
Now, list down the factors of 1746
:1,2,3,6,9,18,97,194,291,582,873,1746
Now, list down the factors of 8684
:1,2,4,13,26,52,167,334,668,2171,4342,8684
Greatest Common Factor
We found the factors 1746,8684 . The biggest common factor number is the GCF number.
So the greatest common factor 1746,8684 is 2.
Lets's calculate LCM of 205,7653
Given numbers has no common factors except 1. So, there LCM is their product i.e 1568865
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1568865
Therefore, the GCF of Fractions 1746/205,8684/7653 is 2/1568865
Least Common Multiple of 205,7653 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 205,7653 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,7653) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,7653) x common factors =1 x 1 = 1
LCM(205,7653) = ( 205 × 7653 ) / 1
LCM(205,7653) = 1568865 / 1
LCM(205,7653) = 1568865
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FAQs on GCF of Fractions of 1746/205, 8684/7653
1. What is the HCF of 1746,8684?
The HCF of 1746,8684 is 2
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 1746/205, 8684/7653?
Answer: GCF of Numerators as per given numbers 1746/205, 8684/7653 is
GCF of Numerators i.e. for 1746,8684 is 2
LCM of denominators i.e. for 205,7653 is 1568865.
Thus, GCF of Fractions is 2/1568865.Finally, GCF of Fractions for 1746/205, 8684/7653 is 2/1568865.