Question

Which positive integers have exactly three positive divisors?​

Answer 1

Answer:

answer should be all the integer a satisfy a = prime^2

Step-by-step explanation:

Answer 2

Which positive integers have exactly three positive divisors is $n = p^2$ , where p is prime

Explanation:

The positive integers are the numbers 1, 2, 3, sometimes called the counting numbers or natural numbers

If N(n) = 3, its prime factorization must not contain more than two primes. If n is itself a prime, N(n) = 2,  so $n = p_1 p_2$. And if $p_1$ not equal to $p_2$, N(n) = 4 since 1, $p_1,p_2,p_1p_2$ are the prime factors. Therefore N(n) = 3 if and  only if $n = p^2$ , where p is a prime.

Whereas for

Which positive integers have exactly four positive divisors? $n = p_1 p_2$, where $p_1$ and   $p_2$ are distinct primes, and $n = q^3$, where q is  prime.

If  N(n) = 4, then its prime factorization must contain more than one and less than four prime  factors. If it has two prime factors, then these factors must be distinct: $n = p_1 p_2$, $p_1$ is not equal to $p_2$, in which case  N(n) = 4 (the divisors being 1, $p_1,p_2,p_1p_2$); and if it has three prime factors, with at least two distinct, then  N(n) ≥ 5, so it must be $n = p^3$ , where p is a prime. We conclude that N(n) = 4 if and only if $n = p_1 p_2$ for  distinct primes $p_1,p_2$, or $n = p^3$where p is prime.

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