# Number Theory

1. Which positive integers have the property that they are divisible by all the positive integers up to and including half their value?

Very quickly you work out that the largest number you can find that exhibits this property is 6 but so far I haven't been able to prove mathematically why this is true. Can anyone explain?
2. (Original post by QuantumQuibit)
Which positive integers have the property that they are divisible by all the positive integers up to and including half their value?

Very quickly you work out that the largest number you can find that exhibits this property is 6 but so far I haven't been able to prove mathematically why this is true. Can anyone explain?
You'll get more answers to this if you post it in the mathematics forum, rather than the maths course forum. But for the meantime, think about how large the product of the first few primes gets.

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