# maths help

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The factors for 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

grouped by last digit {1},{2, 12, 52},{3,13},{4},{6, 26, 156},{78},{39}

Fenders are defined as factor enders. For example the fenders (factor enders) of 156 are 1, 2, 3, 4, 6, 8, 9 and that 156 is a 7-fender (that is, it has seven fenders).

(Question 1)

Show that a number which has 0 and 9 as fenders has at least four more fenders.

(Question 2)

The smallest 10-fender is less than 700. Find it and explain why it is the smallest.

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Ok, let's see if this helps.

(Question 1)

Show that a number which has 0 and 9 as fenders has at least four more fenders.

If a number has 0 and 9 as fenders then it must be divisible by 10 and 9, because you can't divide by 0 and 9 is the first number that ends with 9. Now:

- divisible by 10$\Longrightarrow$divisible by 2 and by 5

- divisible by 9$\Longrightarrow$divisible by 3

Until now you have 3 more fenders {2,3,5}, and the other is 1.

So the fenders are {1,2,3,5}, four at least.

Question 2, coming soon

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• 1 month later...

Hi,

I have the same maths question and I am in year 7.

I have the answer to question 2.

I chose 1,4,5,27 and multiplied all of them together.

The 1 for the 1 fender

The 4 for the 2 and 4 fender (even numbers are divisible by 2)

The 5 for the 5 and 0 fender (even numbers multiplied by 5 results in a multiple of 10)

The 27 for the 3, 6, 7, 8 and 9 fender

27 multiplied by an even number would result it being divisible by 6 and 18.

The factors of 6 is 3 and 2, the factors of 18 is 3, 3, 2.

If you could, could you help me with a question?

(Question 3)

Find three 9-fenders less than 1000 with different sets of fenders.

I already have 360, and I could have had 720 and 900 if the question had not asked for the fender sets to be different...

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• 2 weeks later...
Ok' date=' let's see if this helps.

If a number has 0 and 9 as fenders then it must be divisible by 10 and 9, because you can't divide by 0 and 9 is the first number that ends with 9. Now:

- divisible by 10[math']\Longrightarrow[/math]divisible by 2 and by 5

- divisible by 9$\Longrightarrow$divisible by 3

Until now you have 3 more fenders {2,3,5}, and the other is 1.

So the fenders are {1,2,3,5}, four at least.

Question 2, coming soon

Your explanation is wrong. The FENDER is 9 doesn't mean it is divisible by 9. e.g. it could be divisible by 19.

The reason is that it must have a fender of 8. you work it out why.

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Has anyone got D yet? (I am in year 8 and I am not doing a booklet of some sort and am in Maths Extension) I've got 180, 360, or 720 as you can only use one set of fenders

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I know all the answers so if anyone needs help, ask me.

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