Question

The number n has a total of 10 positive factors (including 1 and n). What is the smallest possible number of factors for n^2?

Answer 1

The number n has a total of 10 positive factors (including 1 and n). What is the smallest possible number of factors for n^2?

we are given n=1,2,3,...n

and  we have to find smallest possible number of factors for n^2

to find smallest number we put one by one

1,2,3,4,....n

in n^2

first of all replace n by 1 in n^2

n^2=1^2=1

n^2=2^2=4

n^2=3^2=9

hence

1 is the smallest possible number of factors for n^2