Question

find the properties of number that the number of factors come as an odd number
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Answer 1

Given :  number of factors come as an odd number

To Find : the properties of number  

Solution:

In general factor are in pairs

Like for a number n

n = a * b  = c * d  =  _____

Hence factors are in even numbers

but if there is one factor

n = k * k    also  with other factor

Then this will be 1 factor  ( odd number )

even + odd =  odd

Hence total number of factors will be odd

n = k ²

Hence number must be a perfect square

properties of number that the number of factors come as an odd number is that Number must be a perfect square

For example

1 = 1²  has only factor   1

4 = 2²  has  3 factors  1 , 2 , 4    

9 = 3²  has 3 factor  1 , 3 , 9

16 = 4²  has 5 factors  1 , 2 , 4 , 8 , 16    

so Perfect square has odd number of factors

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