Number Theory


Divisibility: Level 1 Challenges


Is 93123212 divisible by 4?\large \text{Is } 93123212 \text{ divisible by } 4?

Is 56782431895057 divisible by 11?

The digits 1, 2, 3, 4, and 5 are each used once to compose a five-digit number ABCDE\overline{ABCDE}, such that the three-digit number ABC\overline{ABC} is divisible by 4, BCD\overline{BCD} is divisible by 5 and CDE\overline{CDE} is divisible by 3.

Submit the value of the five-digit number ABCDE\overline{ABCDE} as your answer.

Can an even number, divided by another even number, times another even number ever equal an odd number?

If "yes," then find three numbers that work.
If "no," then why not?

Note that the three even numbers can be different numbers.

What digit, in place of the \square , will make the 8-digit integer, 2345678 2345678 \square a multiple of 6?


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