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 $n?$
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! :)
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! :)