#Numbers-5

When all factors are written in ascending order of N ,product of factors at 8 position and 18 position = N.
Which of the following must be true about N?

1.It is an odd number
2.It is an Even Number
3.It is a Perfect Square
4.CBD





Solution:

Theory:-
lets take an example..Factors of  36?

  Factor:-                          1  2  3  4  6  9  12 18 36 
Position-                        1  2 3  4  5  6   7    8  9
Number of factors=9
Now see that product ...Product of factors which are equidistant from each other form the Number N

 1*36
2*18
3*12
4*9

 Rule:-if the Number of factors are odd it is a Perfect Square

 Now in the question:

 1)product of factors at position (8 and 18) gives the number N .i.e. they are equidistant from each      other.
2)There are 7 factors before 8 ,so there will be 7 factors after 18
Hence, 18 +7=25

 Now 25 is ODD, Hence it is a Perfect Square




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