Discussion

What is the remainder when 13 × 57 × 67 × 78 × 52 is divided by 10?

Answer: D

The remainder is 2.

The remainder on division by 10 is the units digit of the product, and only the units digits of the factors matter: 3, 7, 7, 8 and 2.

\[ \begin{aligned} 3 \times 7 &= 21 \to 1 \\ 1 \times 7 &= 7 \\ 7 \times 8 &= 56 \to 6 \\ 6 \times 2 &= 12 \to 2 \end{aligned} \]

So the product ends in 2. 6 is the units digit one step before the last factor, a sign of dropping the 52. 3 and 8 come from slips in the chain.

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