document.write( "Question 216730: You have 5 consecutive numbers. One of them is 17. What is the ones digit of their product? \n" ); document.write( "
Algebra.Com's Answer #163633 by jsmallt9(3758)\"\" \"About 
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The 5 consecutive numbers either include 20 or not. Let's consider both possibilities:
  • The consecutive numbers include 20.
    • If this is true then the product is some (large) multiple of 20.
    • All multiples of 20 end in a zero.
  • The consecutive numbers do not include 20.
    • If this is true then the numbers must include 15. (Try to find five consecutive numbers that include 17 but not 20 or 15!).
    • Then the product is a (large) multiple of 15.
    • If the product is a multiple of 15 then it is also a multiple of 5.
    • The five consecutive numbers must include at least one even number.
    • When multiplying whole numbers, when at least one number is even, the product will be even.
    • The product will, therefore, be an even multiple of 5.
    • Even multiples of 5 end in 0.

\n" ); document.write( "In summary, the product will either be a multiple of 20 or it will be an even multiple of 5. Either way the product will end in a 0. \n" ); document.write( "
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