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

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) (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) (Show Source): You can put this solution on YOUR website!
It's zero.
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