GCF of 3729/684, 3182/589
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3729/684, 3182/589 i.e 1/21204 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3729/684, 3182/589.
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 3729/684,3182/589?
Given fractions are 3729/684,3182/589
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 3729/684,3182/589, numerators are 3729,3182
Denominators are 684,589
The GCF of 3729,3182 is 1 .
LCM of 684,589 is 21204.
The greatest common factor of 3729/684,3182/589 = [GCF of 3729,3182]/[LCM of 684,589]= 1/21204
Therefore, the GCF of 3729/684,3182/589 is 1/21204.
To find the highest common factor of 3729,3182, we have to find the factors of both numbers and list the highest common factor.
The factors of 3729 are 1, 3, 11, 33, 113, 339, 1243, 3729
The factors of 3182 are 1, 2, 37, 43, 74, 86, 1591, 3182
The HCF of 3729,3182 is 1.
Lets's calculate GCF of 3729,3182
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3729,3182 By Matching Biggest Common Factor Method
Now, list down the factors of 3729
:1,3,11,33,113,339,1243,3729
Now, list down the factors of 3182
:1,2,37,43,74,86,1591,3182
Greatest Common Factor
We found the factors 3729,3182 . The biggest common factor number is the GCF number.
So the greatest common factor 3729,3182 is 1.
Lets's calculate LCM of 684,589
| 19 | 684, 589 |
| 36, 31 |
∴ So the LCM of the given numbers is 19 x 36 x 31 = 21204
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21204
Therefore, the GCF of Fractions 3729/684,3182/589 is 1/21204
Least Common Multiple of 684,589 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 684,589 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,589) = 19
common factors(in case of two or more numbers have common factors) = 1
GCF(684,589) x common factors =19 x 1 = 19
LCM(684,589) = ( 684 × 589 ) / 19
LCM(684,589) = 402876 / 19
LCM(684,589) = 21204
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FAQs on GCF of Fractions of 3729/684, 3182/589
1. What is the HCF of 3729,3182?
The HCF of 3729,3182 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 3729/684, 3182/589?
Answer: GCF of Numerators as per given numbers 3729/684, 3182/589 is
GCF of Numerators i.e. for 3729,3182 is 1
LCM of denominators i.e. for 684,589 is 21204.
Thus, GCF of Fractions is 1/21204.Finally, GCF of Fractions for 3729/684, 3182/589 is 1/21204.