The seven-digit integer is a multiple of (where are digits). Determine all possible ordered pairs .
Source: NCTM Mathematics Teacher, December 2005
Since and , we multiply by , etc. and by , etc. to find the possible digits that would match
Only and are close match of .
We do the same multiplication of by , etc.
Only is a close match
The possible ordered pairs are .
Since , must be divisible by and . To be divisible by the last three digits must be divisible by . To be divisible by the sum of the digits must be divisible by .
and are divisible by
not divisible by
not divisible by 8