Question 216730
The 5 consecutive numbers either include 20 or not. Let's consider both possibilities:<ul><li>The consecutive numbers include 20.<ul><li>If this is true then the product is some (large) multiple of 20.</li><li>All multiples of 20 end in a zero.</li></ul><li>The consecutive numbers do not include 20.<ul><li>If this is true then the numbers must include 15. (Try to find five consecutive numbers that include 17 but not 20 or 15!).</li><li>Then the product is a (large) multiple of 15.</li><li>If the product is a multiple of 15 then it is also a multiple of 5.</li><li>The five consecutive numbers must include at least one even number.</li><li>When multiplying whole numbers, when at least one number is even, the product will be even.</li><li>The product will, therefore, be an even multiple of 5.<li>Even multiples of 5 end in 0.</li></ul></li></ul>
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.