Question : The unit digit in the product $7^{71}\times 6^{59}\times 3^{65}$ is:
Option 1: $1$
Option 2: $2$
Option 3: $3$
Option 4: $4$
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Correct Answer: $4$
Solution : Unit digit of $7^{71}$(Unit digit of $7^{(4)}$ = 1) = Unit digit of $(7^{(4)^(17)} ×7^3) = 3$ Unit digit of $3^{65}$(Unit digit of $3^{(4)}$ = 1) = Unit digit of $(3^{(4)^(16)} \times 3) = 3$ Unit digit of $6^{59} = 6$ Now, unit digit of $7^{71} × 6^{59} × 3^{65} ⇒ 3×6×3 ⇒ 4$ Hence, the correct answer is $4$.
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