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Solve problems using multiples and factorsUsing multiples

Many maths problems involve using multiples and factors to find the answer. If you are set a word problem you should look at the key information given to see if you need to use factors or multiples.

Part of MathsMultiples, factors and primes

Using multiples

Here is an example of a word-based question in maths:

Brian, a lighthouse keeper, switches on the lighthouse light at exactly 9pm. The light rotates in such a way that it looks like it flashes every 8 seconds. This means the first flash appears 8 seconds after 9pm. Susan gets up out of her chair at 9pm, puts the kettle on and looks out of her window at the lighthouse. The time it takes her to reach the window is 57 seconds. If she looks out for 5 seconds, will she see the light flash?

Word-based questions can be long! To help answer this kind of question:

1. Highlight the key information:

Brian, a lighthouse keeper, switches on the lighthouse light at exactly 9pm. The light rotates in such a way that it looks like it flashes every 8 seconds. This means the first flash appears 8 seconds after 9pm. Susan gets up out of her chair at 9pm, puts the kettle on and looks out of her window at the lighthouse. The time it takes her to reach the window is 57 seconds. If she looks out for 5 seconds, will she see the light flash?

This problem involves multiples. The lighthouse flashes every 8 seconds, so the times it flashes are all multiples of 8.

2. Organise the key information:

LighthouseSusan
Starts at 9pm - flashes every 8 secondsStarts at 9pm - gets to window after 57 seconds. Stays there for 5 more seconds.
First flash at 8 secondsArrives at the window at 57 seconds
Next flash at 16 secondsIs at the window at 58 seconds
Next flash at 24 secondsIs at the window at 59 seconds
Next flash at 32 secondsIs at the window at 60 seconds
Next flash at 40 secondsIs at the window at 61 seconds
Next flash at 48 secondsIs at the window at 62 seconds
Next flash at 56 secondsShe stops looking out of the window
Next flash at 64 seconds
Next flash at 72 seconds
LighthouseStarts at 9pm - flashes every 8 seconds
SusanStarts at 9pm - gets to window after 57 seconds. Stays there for 5 more seconds.
LighthouseFirst flash at 8 seconds
SusanArrives at the window at 57 seconds
LighthouseNext flash at 16 seconds
SusanIs at the window at 58 seconds
LighthouseNext flash at 24 seconds
SusanIs at the window at 59 seconds
LighthouseNext flash at 32 seconds
SusanIs at the window at 60 seconds
LighthouseNext flash at 40 seconds
SusanIs at the window at 61 seconds
LighthouseNext flash at 48 seconds
SusanIs at the window at 62 seconds
LighthouseNext flash at 56 seconds
SusanShe stops looking out of the window
LighthouseNext flash at 64 seconds
Susan
LighthouseNext flash at 72 seconds
Susan

3. Use that information to work out the answer to the question:

Question

Will Susan see the lighthouse light flash?

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Using factors

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