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    Question

    Find the unit digit in (257)45 ×

    (248)73.
    A 3 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 2 Correct Answer Incorrect Answer

    Solution

    To find the units digit of (257)45 x (248)773: Units digit of 257 is 7. The pattern for powers of 7 (7, 9, 3, 1) repeats every 4. Since 45 mod 4 = 1, the units digit of 745 is 7. Units digit of 248 is 8. The pattern for powers of 8 (8, 4, 2, 6) repeats every 4. Since 73 mod 4 = 1, the units digit of 873 is 8. Multiply the results: 7 x 8 = 56. Unit digit =6.

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