GCF of 2065/414, 3615/5832
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2065/414, 3615/5832 i.e 5/134136 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2065/414, 3615/5832.
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 2065/414,3615/5832?
Given fractions are 2065/414,3615/5832
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 2065/414,3615/5832, numerators are 2065,3615
Denominators are 414,5832
The GCF of 2065,3615 is 5 .
LCM of 414,5832 is 134136.
The greatest common factor of 2065/414,3615/5832 = [GCF of 2065,3615]/[LCM of 414,5832]= 5/134136
Therefore, the GCF of 2065/414,3615/5832 is 5/134136.
To find the highest common factor of 2065,3615, we have to find the factors of both numbers and list the highest common factor.
The factors of 2065 are 1, 5, 7, 35, 59, 295, 413, 2065
The factors of 3615 are 1, 3, 5, 15, 241, 723, 1205, 3615
The HCF of 2065,3615 is 5.
Lets's calculate GCF of 2065,3615
| 5 | 2065, 3615 |
| 413, 723 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 2065,3615 By Matching Biggest Common Factor Method
Now, list down the factors of 2065
:1,5,7,35,59,295,413,2065
Now, list down the factors of 3615
:1,3,5,15,241,723,1205,3615
Greatest Common Factor
We found the factors 2065,3615 . The biggest common factor number is the GCF number.
So the greatest common factor 2065,3615 is 5.
Lets's calculate LCM of 414,5832
| 2 | 414, 5832 |
| 3 | 207, 2916 |
| 3 | 69, 972 |
| 23, 324 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 324 = 134136
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/134136
Therefore, the GCF of Fractions 2065/414,3615/5832 is 5/134136
Least Common Multiple of 414,5832 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 414,5832 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,5832) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(414,5832) x common factors =18 x 1 = 18
LCM(414,5832) = ( 414 × 5832 ) / 18
LCM(414,5832) = 2414448 / 18
LCM(414,5832) = 134136
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FAQs on GCF of Fractions of 2065/414, 3615/5832
1. What is the HCF of 2065,3615?
The HCF of 2065,3615 is 5
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 2065/414, 3615/5832?
Answer: GCF of Numerators as per given numbers 2065/414, 3615/5832 is
GCF of Numerators i.e. for 2065,3615 is 5
LCM of denominators i.e. for 414,5832 is 134136.
Thus, GCF of Fractions is 5/134136.Finally, GCF of Fractions for 2065/414, 3615/5832 is 5/134136.