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Home/ Questions/Q 1553
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Fathimafarhani
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FathimafarhaniBegginer ( Level 6 )
Asked: February 26, 20232023-02-26T14:30:43+05:30 2023-02-26T14:30:43+05:30In: Algebra ( වීජ ගණිතය )

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  • What is the last digit of 2^2015 ?
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  1. Janaka Rodrigo Level 3 English medium advanced level mathematics teacher at St Benedicts College Colombo 13
    2023-02-26T19:50:28+05:30Added an answer on February 26, 2023 at 7:50 pm

    If you check the powers of 2 such as 2,4,8,16,32,64,128,256,…, you can find the pattern of the last digit 2,4,8,6,2,4,8,6,… which has a repeated sequence of period of 4 . Now you can divide the power by 4 and if it gives remainder as 1 last digit is 2 , if the remainder is 2 last digit is 4 , if the remainder is 3 last digit is 8 and if the remainder is 0 last digit is 6.

    In your case the power 2015 divided by 4 gives remainder 3 . Therefore last digit should be 8. Hope this way may be helpful to solve your problem.

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