Factorize?

All the numbers of the form 6^n end with 6. That is the simplest solution I can think of.

$2^{n} \times 3^{n}$

$= (2 \times 3)^{n}$

$=6^{n}$

Now $6^{n}$ must end in the digit 6 because of the following:

$6^{n}$

$=6 \times (5+1)^{n-1}$

$=6 \times$ ( $5^{n-1}$ + $[n-1] \times 5^{n-2}$ ... $+1$ )

Since $6 = 2 \times 3$ , whenever a 6 is multiplied by a multiple of 5 it will be a multiple of 10 ( $2 \times 5$ ) and hence will have no effect on the final digit. This means that the only term from within the brackets that has any effect on the final digit is the ...+1 at the end. And since $6 \times 1 = 6$ . Then $6^{n}$ must end in a 6. The only option with 6 as a final digit is 60466176 hence this must be the correct answer.