SOLUTION: You have 5 consecutive numbers. One of them is 17. What is the ones digit of their product?

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Question 216730: You have 5 consecutive numbers. One of them is 17. What is the ones digit of their product?
Found 2 solutions by jsmallt9, Alan3354:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
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.

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.

Answer by Alan3354(69443) About Me  (Show Source):