Step 1: Idea:
Three numbers are alike in some way. We look at their factors rather than their digits.
Step 2: Use the divisibility test for 3:
A number is divisible by 3 when the sum of its digits is divisible by 3. For 23 the sum is 5, for 43 it is 7, for 73 it is 10, and for 93 it is 12.
Step 3: Read the result:
Only 93 has a digit sum that is a multiple of 3, so only 93 can be divided by 3. That gives 93 = 3 x 31.
Step 4: Confirm the rest:
23, 43 and 73 have no small divisors up to their square roots (about 4.8, 6.6 and 8.5), so they are primes. So 93 is the odd one.
Final Answer:
The odd number is 93.
\[ \boxed{93} \]