<s>[INST] Number of divisors of the number $2079000$ which are even and divisible by $15$ 
Find the number of divisors of $2079000$ which are even and divisible by $15$?

My Attempt: Since they are divisible by $15$ and are even, $2$ and $5$ have to included from the numbers prime factors.
$2079000 = 2^3 \cdot 3^3 \cdot 5^3 \cdot 7 \cdot 11$
Therefore, the number of divisors should be 
$2 \cdot 2 \cdot (3+1) \cdot (1+1) \cdot (1+1)$
But however this answer is wrong.
Any help would be appreciated.
 [/INST] You should simplify a 2, a 3, and a 5. This is equivalent to find the number of positive divisors of
$$
\frac{2079000}{30} = 69300 = 2^2 \cdot 3^2\cdot 5^2\cdot 7\cdot 11
$$
which is 
$
3^3 \cdot 2^2.
$
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