To find the unit digit of the product 13 * 27 * 63 * 51 * 98 * 46, we should focus only on the unit digits of these numbers:
Now, multiply these unit digits:
3 (unit digit of 13) * 7 (unit digit of 27) = 21, unit digit is 1.
1 (from previous step) * 3 (unit digit of 63) = 3, unit digit is 3.
3 (from previous step) * 1 (unit digit of 51) = 3, unit digit is 3.
3 (from previous step) * 8 (unit digit of 98) = 24, unit digit is 4.
4 (from previous step) * 6 (unit digit of 46) = 24, unit digit is 4.
The unit digit of the entire product is therefore 4.
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: