I. N is a 3-digit number abc.
ii. a,b,c are distinct non-zero decimal digits.
iii. The product a*b*c divides N.

List all possible values for (a,b,c) complying with the above conditions.

Call the divisor, d. d must be between 1 and 9, since abc/10 will be less than 100.

Then for:

d=4: 384=4*3*8*4

d=7: 735=7*7*3*5

d=8: 128=8*1*2*8, 672=8*6*7*2

d=9: 135=9*1*3*5, 144=9*1*4*4

**Ugh. Correction! d can be more than 10, so please ignore the above.**

Edited on January 15, 2015, 3:13 am

Posted by broll on 2015-01-14 18:29:21