Factor List

Age 14 to 16

ShortChallenge Level Yellow star

Answer: there are 2 possible values for

$N$ (

$90$ or

$405$ )

Factors come in pairs with product

$N$ :

So

$f\times45f=N\Rightarrow N=45f^2$ .

$f$ must be prime because factors of

$f$ are also factors of

$N$

Factors of

$45$ are also factors of

$N$ so

$3$ and

$5$ are factors of

$N$

$f\le3$ so

$f=2$ or

$f=3$

So

$N=45\times2^2=90$ or

$N= 45\times 3^2 = 405$

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

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