Products and divisibility
Number Theory
Level
2
The product of any 5 consecutive positive integers must be divisible by which of the following numbers?
All of 2, 3, 4, 5, 6
2 only
3 only
4 only
5 only
6 only
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In a list of consecutive numbers; every other number is divisible by 2, every 3rd number is divisible by 3, and etc.
Thus, the product of 5 consecutive integers has at least 1 factor of 2, 3, 4, and 5.
Being divisible by 2 and 3 also means the number is divisible by 6