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

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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.