If a number n has exactly 7 divisors, how many divisors

Ответ:

angelteddy033

03.01.2022

Mathematics

A number $n=p_1^{a_1}\cdot p_2^{a_2}\cdot\ldots\cdot p_k^{a_k}$ , where p_k

are distinct prime numbers, has $(a_1+1)(a_2+1)\cdot\ldots\cdot(a_k+1)$ divisors.

We know that

has 7 divisors. 7 is a prime number, so among the numbers $a_1+1,a_2+1,\ldots,a_k+1$ there is only one that is equal to 7.

So,
$a_k+1=7\\
a_k=6$

That means n=p^6

where

is a prime number.
$n^2=(p^6)^2=p^{12}$ , therefore the n^2

has

divisors.

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Ответ:

ashleydawn6430

15.02.2021

Mathematics

As you can see point E is not on neither of those lines

Hope this helps :D

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If a number n has exactly 7 divisors, how many divisors does n squared have?

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