Is 2003 divisible by 3?

Hello!

No, 2003 isn't divisible by 3. Strictly speaking, there is no such integer that  although such rational number exists.

To prove this, express 2003 as 3*667 + 2, which means the remainder of division of 2003 by 3 is 2. If 2003 would divisible by 3, then

2 = 2003 - 3*667

would be also divisible by 3, which is false.

Also there is a simple divisibility rule: a decimal integer N is divisible by 3 if and only if the sum of digits of N is divisible by 3.

The cause of this rule is that 10 gives the remainder 1 after division by 3. Therefore 100, 1000 and all other powers of 10 give the remainder 1 after division by 3.

In our case 2003 becomes 2+0+0+3=5, which isn't divisible by 3.