Find unit digit of product (173)45 × (152)77 × (777)999.
A. 4
B. 2
C. 8
D. 6
E. None of these
Answer: Option C
Solution(By Examveda Team)
To find unit digit of a number or an Expression, We have to divide the number or expression by 10 and the remainder obtained by this operation would be the required unit digit.$$\eqalign{ & \frac{{ {{{\left( {173} \right)}^{45}} \times {{\left( {152} \right)}^{77}} \times {{\left( {777} \right)}^{999}}} }}{{10}} \cr & {\text{Remainder}}\,{\text{would}}\,{\text{be}}\,{\text{same}}\,{\text{as}}, \cr & \frac{{ {{3^{45}} \times {2^{77}} \times {7^{999}}} }}{{10}} \cr & Or,\,\frac{{ {3 \times 2 \times {7^3}} }}{{10}} \cr & Or,\,\frac{{ {6 \times 343} }}{{10}} \cr & {\text{Remainder}}\,{\text{would}}\,{\text{be}}\,{\text{same}}\,{\text{as}}\,\frac{{ {6 \times 3} }}{{10}} \cr }$$
Thus, Required remainder and unit digit will be 8.
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