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Remainders

Age 7 to 11 Challenge Level:

There is an updated version of this task here.


Here is a chance to explore some properties of numbers and then have a go at some questions.

The interactivity below allows you to choose a divisor and then select numbers in one of the columns.

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.

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Now try out the problem generator below. When you click "Start" the computer will select at random an integer between 1 and 100. Can you identify the chosen number?

You can use the interactivity above to help you, but eventually, try to identify the numbers without the aid of the interactivity.


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One final question:

We know that

When 59 is divided by 5, the remainder is 4
When 59 is divided by 4, the remainder is 3
When 59 is divided by 3, the remainder is 2
When 59 is divided by 2, the remainder is 1

Can you find the smallest number with the property that when it is divided by each of the numbers 2 to 10, the remainder is always one less than the number it is has been divided by? Don't forget to explain your reasoning.