GCF of 2405/164, 3645/2018
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2405/164, 3645/2018 i.e 5/165476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2405/164, 3645/2018.
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 2405/164,3645/2018?
Given fractions are 2405/164,3645/2018
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 2405/164,3645/2018, numerators are 2405,3645
Denominators are 164,2018
The GCF of 2405,3645 is 5 .
LCM of 164,2018 is 165476.
The greatest common factor of 2405/164,3645/2018 = [GCF of 2405,3645]/[LCM of 164,2018]= 5/165476
Therefore, the GCF of 2405/164,3645/2018 is 5/165476.
To find the highest common factor of 2405,3645, we have to find the factors of both numbers and list the highest common factor.
The factors of 2405 are 1, 5, 13, 37, 65, 185, 481, 2405
The factors of 3645 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, 729, 1215, 3645
The HCF of 2405,3645 is 5.
Lets's calculate GCF of 2405,3645
| 5 | 2405, 3645 |
| 481, 729 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 2405,3645 By Matching Biggest Common Factor Method
Now, list down the factors of 2405
:1,5,13,37,65,185,481,2405
Now, list down the factors of 3645
:1,3,5,9,15,27,45,81,135,243,405,729,1215,3645
Greatest Common Factor
We found the factors 2405,3645 . The biggest common factor number is the GCF number.
So the greatest common factor 2405,3645 is 5.
Lets's calculate LCM of 164,2018
| 2 | 164, 2018 |
| 82, 1009 |
∴ So the LCM of the given numbers is 2 x 82 x 1009 = 165476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/165476
Therefore, the GCF of Fractions 2405/164,3645/2018 is 5/165476
Least Common Multiple of 164,2018 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 164,2018 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,2018) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,2018) x common factors =2 x 1 = 2
LCM(164,2018) = ( 164 × 2018 ) / 2
LCM(164,2018) = 330952 / 2
LCM(164,2018) = 165476
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FAQs on GCF of Fractions of 2405/164, 3645/2018
1. What is the HCF of 2405,3645?
The HCF of 2405,3645 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 2405/164, 3645/2018?
Answer: GCF of Numerators as per given numbers 2405/164, 3645/2018 is
GCF of Numerators i.e. for 2405,3645 is 5
LCM of denominators i.e. for 164,2018 is 165476.
Thus, GCF of Fractions is 5/165476.Finally, GCF of Fractions for 2405/164, 3645/2018 is 5/165476.