The unit's digit in the product $274 \times 318 \times 577 \times 313$ is

### Concept & Strategy The unit digit of a product of multiple numbers is simply the unit digit of the product of their individual unit digits. The tens, hundreds, and higher-place digits have zero effect on the final unit digit. ### Step-by-Step Solution **Given:** The product expression is $274 \times 318 \times 577 \times 313$. **Calculation:** * Extract only the unit digits of each number: $4, 8, 7,$ and $3$. * Multiply them sequentially, keeping only the unit digit at each step to simplify math: * Step 1: $4 \times 8 = 32 \rightarrow$ Unit digit is $2$. * Step 2: $2 \times 7 = 14 \rightarrow$ Unit digit is $4$. * Step 3: $4 \times 3 = 12 \rightarrow$ Unit digit is $2$. * The final unit digit is $2$. ### Exam Strategy & Shortcut Group the numbers to make multiplication even faster. Multiply the first pair ($4 \times 8 = 32 \rightarrow 2$) and the second pair ($7 \times 3 = 21 \rightarrow 1$). Then multiply their results: $2 \times 1 = 2$. This avoids carrying large intermediate numbers in your head. ### Common Pitfall Multiplying the entire numbers out fully or carrying two-digit intermediate products (like $32 \times 21 = 672$) wastes valuable exam time and increases the risk of basic arithmetic errors. Always strip down to single digits immediately. ### Final Answer **Therefore, the correct answer is 2.**