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March 26, 2017

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The unit's digit for the number 7^76 is____ ?

  • MATH - ,

    look at powers of 7
    7^0 ends in 1
    7^1 ends in 7
    7^2 ends in 9
    7^3 ends in 3
    7^4 ends in 1
    7^5 ends in 7
    7^6 ends in 9
    etc.

    So it repeats after 4 digits
    If we divide the exponent by 4, all we have to do is look at the remainder, and match it with the exponents of the above chart.

    eg. for 7^10 (your calculator can still do that one)
    it ends in????
    10÷4 leaves a remainder of 2 and from the above, for an exponent of 2 our number should end in 9
    10^7 ends in a 9 !!!

    So...
    for 7^76 , dividing 76 by 4 leaves a remainder of 0
    so 7^76 end in 1

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