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A number n has 3 divisors. How many divisors does $n^3$ have?

 Oct 20, 2021
 #1
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+1

n ==9

(1, 3, 9)>>Total = 3 divisors

 

9^3==729

(1, 3, 9, 27, 81, 243, 729)>>Total = 7 divisors

 Oct 20, 2021
 #2
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+1

n has 3 divisors, these muct be 1, itself and one other, which means that n is a perfect square (of a prime number)

so

n=a^2 where a is prime

 

n^3=(a^2)^3 = a^6

 

This will have 6+1=7 factors (divisors)

 Oct 20, 2021

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