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\(\displaystyle 21600=2\cdot5\left(2^4\cdot3^3\cdot5 \right)= 10\cdot2^4\cdot3^3\cdot5\)

Now looking at the factor to the right of 10, consider a divisor of 21600 of the form:

\(\displaystyle 2^{n_1}\cdot3^{n_2}\cdot5^{n_3}\)

What are the number of choices we have for the parameters $n_i$ such that this factor is not divisible by 3? Then apply the fundamental counting principle. What do you find?