+1222 A positive integer is called nice if it is a multiple of $6.$
A certain nice positive integer $n$ has exactly $8$ positive divisors. How many prime numbers are divisors of $n?$
+1908 If a number is divisble by 6, then it is also divisble by \(1,2,3,6\)
Now, let's take a look at factors of 6.
We know that \(12\) has 6 factors, as we have \(1,2,3,4,6,12\)
18 also 6 factors, as we have \(1,2,3,6,9,18\)
However, 24 has exactly 8 factors. We have
\(1,2,3,4,6,8,12,24\)
The prime factors are \(2,3\), so our answer is just 2.
So there are 2 prime factors.
Thanks! :)
+1908 If a number is divisble by 6, then it is also divisble by \(1,2,3,6\)
Now, let's take a look at factors of 6.
We know that \(12\) has 6 factors, as we have \(1,2,3,4,6,12\)
18 also 6 factors, as we have \(1,2,3,6,9,18\)
However, 24 has exactly 8 factors. We have
\(1,2,3,4,6,8,12,24\)
The prime factors are \(2,3\), so our answer is just 2.
So there are 2 prime factors.
Thanks! :)
