In the following problems provide a complete explanation of whyit is true(1) Letnbe an integer. Justify the followingstatements.(a) The last digit ofnis even if and only ifnisdivisible by 2.(b) The last two digits ofnare divisible by 4 if andonly ifnis divisible by 4.(c) The last three digits ofnaredivisible by 8 if and only ifnis divisible by 8.(d) The lastkdigitsofnare divisible by 2kif and only ifnis divisible by 2k.(2) Letnbean integer. Justify the following statements.(a) The integernisdivisible by 3 if and only if the sum of the digits is divisible by3.(b) The integernis divisible by 9 if and only if the sum of thedigits is divisible by 9.(3) What is the last nonzero digit at theend of 10! ? What is the last nonzero digit at the endof 100! ?What is the last nonzero digit at the end of 1,000,000! ? Describea procedure forfinding the last non-zero digit at the end ofn! foranyn. Use that procedure to find thelast non-zero digit for thefactorial of your student id number
