In this number classification question based on divisibility by 9, select the odd number from the given alternatives.

Introduction / Context:
This quantitative aptitude question checks your understanding of the divisibility rule for 9. Each option is a three digit number, and you have to select the one that does not share the same divisibility property as the others. Using digit sum rules is a fast and effective strategy for solving such questions, which often appear in competitive exams to test number sense.

Given Data / Assumptions:
- The numbers are 153, 261, 104, and 108.- All are positive integers with three digits.- We will apply the divisibility rule for 9.

Concept / Approach:
The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is a multiple of 9. This rule is simple to apply, especially for medium sized numbers, and it avoids long division. If three numbers satisfy this rule and one does not, then that one is the odd number. Let us apply the rule systematically.

Step-by-Step Solution:
Step 1: For 153, the digit sum is 1 + 5 + 3 = 9, which is a multiple of 9. So 153 is divisible by 9.Step 2: For 261, the digit sum is 2 + 6 + 1 = 9, again a multiple of 9. So 261 is divisible by 9.Step 3: For 108, the digit sum is 1 + 0 + 8 = 9, also a multiple of 9. So 108 is divisible by 9.Step 4: For 104, the digit sum is 1 + 0 + 4 = 5, which is not a multiple of 9. Therefore, 104 is not divisible by 9.Step 5: Thus, three numbers are multiples of 9 and one is not.

Verification / Alternative check:
You may also check by direct division. 153 divided by 9 equals 17, 261 divided by 9 equals 29, and 108 divided by 9 equals 12. All results are whole numbers. However, 104 divided by 9 gives a non integer result, confirming that 104 is not a multiple of 9.

Why Other Options Are Wrong:
153: Clearly divisible by 9 and fits the group.261: Also a multiple of 9 and belongs with 153 and 108.108: Again, divisible by 9 and not the odd one.

Common Pitfalls:
Students sometimes mix the rules for 3 and 9. Remember that the digit sum must be a multiple of 9, not just of 3, to guarantee divisibility by 9.

Final Answer:
The odd number is 104 because it is not divisible by 9, whereas 153, 261, and 108 are all multiples of 9.