Number System
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Q.

If $N=2^3×3^4$ , $M= 2^2×3×5$, then find the number of factors of $N$ that are common with the factors of $M$.

 A.

8

 B.

6

 C.

18

 D.

20

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Solution:
Option(B) is correct

The factors that are common must also be the factors of $HCF(N,M)$

$HCF(N,M) = 2^2×3$

Number of factors of $2^2×3 = (2+1)(1+1) = 6$

So there are 6 factors that are common to both.


(4) Comment(s)


Shashiii Ghanekar
 ()

N=2^3×3^4=648

M= 2^2×3×5=60

N=648/6=108

M=60/6=10

Therefore 6 is the common factor of 648 and 60 i.e. N and M



Saikiran
 ()

Taking the common values 2^2*3, we get 12.. factors of 12 are 1,2,3,4,6,12.. 6 factors common to M & N.. Is it right too??.. I have a doubt



Abhay
 ()

The answer, I reckon, should be 6. The calculation of HCF is wrong.



Shreya
 ()

is there some problem in the soln as while taking out the hcf we take the less powers of common prime factors