What is the unit digit in the multiplication of $1 \times 3 \times 5 \times 7 \times 9 \times \ldots \times…
What is the unit digit in the multiplication of $1 \times 3 \times 5 \times 7 \times 9 \times \ldots \times 999$?
1
3
5
9
Solution
The product is of all odd numbers from 1 to 999. This product includes the factor 5 (and 15, 25, ...). Any product of odd numbers that contains a multiple of 5 ends in the digit 5, because 5 multiplied by any odd number always ends in 5. Hence the unit digit is 5.