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## 'Remainders' printed from http://nrich.maths.org/

**Example 1:**

Divide by 4 and select all the numbers in the right-hand column - they should all turn red.

Now divide by 5 and select all the numbers in the right-hand column - they should all turn yellow, but some will turn orange.

What is special about the numbers that turn orange?

Now divide by 3 and select all the numbers in the right-hand column - most should turn blue, but one will turn black.

What is special about the number that turns black?

What is special about the numbers that turn green and purple?

**Example 2:** (you will need to clear your previous work)

Find the numbers that have a remainder of 2 when divided by 5 - you'll need to divide by 5 and select the numbers in the second column.

Now select the numbers that have a remainder of 1 when divided by 2 (the odd numbers).

What is special about the numbers that turned orange this time?

Try a few examples of your own and try to predict what will happen in each case.