8448 is a multiple of 44. Change the two 4s for different odd numbers X and Y, so 8XY8 can be divided by XY. No computers allowed!

8138, 8918, 81378, 890918, 89090918....

As Gamer & DJ noted, factorizaion of 8008 can provide the odd prime factors that is or makes up a composite number or prime that must be a factor of both 8XY8 and XY.

The odd primes of 8008 are 7, 11, and 13.  The following are two digit primes or composite numbers that are both odd that can be formed or provided from the odd primes of 8008.

11; 13; 77 ( = 7*11);  and 91 (= 7*13)

As a third condition requires that the numbers be different, 11 & 77 are eliminated, leaving only 13 and 91.  Both of which can be separated into two odd numbers. 

X=1, Y=3 (X||Y = 13)  --> 8138
X=9, Y=1 (X||Y = 91)  --> 8918

(The two pipes, ||, are used as the concatenation symbol to indicate XY is not X*Y, but a concatenation of X and Y).

Yet these two pairs of numbers are not the only solutions.  The problem did not ask for single digit numbers, only different and odd numbers.  Thus there may be and is many more possible answers. 

The odd prime factors of 80008 are 73 and 137. To produce a 3 digit odd number we have but 137.  137 can be separted as two different odd numbers in two distinct ways:

X=1, Y=37 (X||Y = 137)
X=13, Y=7 (X||Y = 137)  --> 81378

For 800008 the odd prime factors are 11 and 9091.  The only 4-digit odd prime or composite therefore is 9091. 9091 can be separated into two odd different numbers as follows:

 X=909 & Y=1 (X||Y = 9091) --> 890918

For 80000008 the odd prime factors are 11 and 909091.  The only 6-digit odd composite is 909091. 909091 can be separated into two odd different numbers as follows:

 X=90909 & Y=1 (X||Y = 909091) --> 89090918

And so forth....

Edited on May 8, 2006, 7:35 pm

Posted by Dej Mar on 2006-05-08 02:26:48