How many divisors of $8!$ divide exactly in $2$ numbers from $\{6,10,12,21\}$

How many divisors of $8!$ divide exactly in $2$ numbers from $\{6,10,12,21\}$

I want to check how many divisors of $8!$ divide exactly in $2$ numbers
from $\{6,10,12,21\}$
first I tried to write $8!$ as $8\cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3
\cdot 2 \cdot 1 = 2^3 \cdot 7 \cdot 2 \cdot 3 \cdot 5 \cdot 2^2 \cdot 3
\cdot 2 \cdot 1 = 2^7 \cdot 7 \cdot 5\cdot 3^2 \cdot 1$
how should I continue ?
Thanks!