You may also like

problem icon

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

problem icon

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

problem icon

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Factor List

Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Let the smallest prime factor of N be p, whence the second largest factor, and the highest factor tina wrote down, is ${N}\over{p}$.
Now we have $\frac{N}{p}= 45p$. So ${N}= 45 p^2$.
Since N is a multiple of $45$, it has prime factors of $3$ and $5$ and, because p is the smallest prime factor of N, we can conclude that p can be only $2$ or $3$.

Hence either $N = 45\times 2^2 = 180$ or $N = 45\times 3^2 = 405$

This problem is taken from the UKMT Mathematical Challenges.