challenge for programmable calculators

[Don Shepherd]

Well, it's a rainy day outside, how about a new challenge for a new forum.

Find a 3-digit number (or numbers) abc such that the sum of the digits times the product of the digits equals the original number. Or, mathematically, a 3-digit number abc such that (a+b+c) X (a X b X c) = abc. The number 000 doesn't count.

All programmable calculator solutions are welcomed, including RPN, RPL, BASIC, Prime, 34s, and even non-HP programmable calculators.

The brute-force solution is relatively easy. A non-brute-force solution would greatly enlighten this rainy day.