Problem E

Four Numbers

Norbert has four favourite numbers. Each of these is a three-digit number \(ABC\) with the following two properties:

The digits \(A\), \(B\), and \(C\) are all different.

The product \(A \times B \times C\) is equal to the two-digit number \(BC.\)

For example, one of Norbertâ€™s favourite numbers is \(236\), since \(2 \times 3 \times 6 = 36.\)

Find Norbertâ€™s other three favourite numbers.

Note: It may be helpful to recall that any two-digit number of the form \(BC\) can be represented by the sum \(10B + C.\) For example, \(32 = 10(3) + 2.\)