GCF of 609/585, 3684/1968
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 609/585, 3684/1968 i.e 3/383760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/585, 3684/1968.
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 609/585,3684/1968?
Given fractions are 609/585,3684/1968
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 609/585,3684/1968, numerators are 609,3684
Denominators are 585,1968
The GCF of 609,3684 is 3 .
LCM of 585,1968 is 383760.
The greatest common factor of 609/585,3684/1968 = [GCF of 609,3684]/[LCM of 585,1968]= 3/383760
Therefore, the GCF of 609/585,3684/1968 is 3/383760.
To find the highest common factor of 609,3684, we have to find the factors of both numbers and list the highest common factor.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 3684 are 1, 2, 3, 4, 6, 12, 307, 614, 921, 1228, 1842, 3684
The HCF of 609,3684 is 3.
Lets's calculate GCF of 609,3684
| 3 | 609, 3684 |
| 203, 1228 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 609,3684 By Matching Biggest Common Factor Method
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 3684
:1,2,3,4,6,12,307,614,921,1228,1842,3684
Greatest Common Factor
We found the factors 609,3684 . The biggest common factor number is the GCF number.
So the greatest common factor 609,3684 is 3.
Lets's calculate LCM of 585,1968
| 3 | 585, 1968 |
| 195, 656 |
∴ So the LCM of the given numbers is 3 x 195 x 656 = 383760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/383760
Therefore, the GCF of Fractions 609/585,3684/1968 is 3/383760
Least Common Multiple of 585,1968 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 585,1968 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,1968) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(585,1968) x common factors =3 x 1 = 3
LCM(585,1968) = ( 585 × 1968 ) / 3
LCM(585,1968) = 1151280 / 3
LCM(585,1968) = 383760
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FAQs on GCF of Fractions of 609/585, 3684/1968
1. What is the HCF of 609,3684?
The HCF of 609,3684 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 609/585, 3684/1968?
Answer: GCF of Numerators as per given numbers 609/585, 3684/1968 is
GCF of Numerators i.e. for 609,3684 is 3
LCM of denominators i.e. for 585,1968 is 383760.
Thus, GCF of Fractions is 3/383760.Finally, GCF of Fractions for 609/585, 3684/1968 is 3/383760.