Number System

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Chandan's picture
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If a natural no n has 12 factors,then which of the following is not a possible value for the no. of factors of n^2. 1.23 2.33 3.45 4.55 5.35

nishit's picture
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Qood one.After the first

Qood one.

After the first look i thought it shd be 23 , but after calculating for all the possible factors I found the answer is 55. (option d).

as soon as i get some time I 'll put the solution

 

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nishit's picture
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Here it goes . . .

A number  N= am x bn x cq

Has (m + 1) (n + 1) (q + 1 ) number of divisors
 
Number of divisors is given as 12
12 = 4 x 3 = ( m+ 1)(n + 1)
So m and n are 3 ,2
After square mand n : 6 , 4
(m+ 1 )and n (+ 1) : 7 , 5
Number of divisor = 7 x 5 = 35
 
12= 12 x 1
11 0
22 0
23 1
Number of divisors = 23
 
12= 6 x 2
5 1
10 2
11 3
Number of divisors =  33
 
12 = 2 x 2 x 3
1 1 2
2 2 4
3 3 5
Number of divisors =  45
 

So the answer is  55

 

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