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Divide it Out

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Divide it Out


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Why do this problem?

This problem requires logical thinking about factors and much multiplication! Learners must first find out what is the lowest number which divides exactly by all the numbers from $2$ to $10$ and then decide how this helps to answer the question asked. A calculator could be useful for checking.

Key questions

How are you going to start on this problem?
Why not start by listing all the numbers from $2$ to $10$?
Which numbers do you not need because they are factors of other numbers you are using?

Possible extension

Learners could find the lowest number which always leaves a remainder of $1$ when divided by any of the numbers from $2$ to $12$, or $2$ to $20$, etc.

Possible support

Suggest starting by finding the lowest number which divides exactly by all the numbers from $2$ to $6$. A calculator might be very helpful.