In the following number classification question, four numbers are given (170, 290, 360 and 530). Three of these are 10 times a prime number, while one is not of that form. Select the odd number from the given alternatives.

Introduction / Context:
This question comes from the number reasoning and classification section. The numbers 170, 290, 360 and 530 all end with a zero, suggesting that each might be 10 times some smaller integer. In three of these cases, the smaller integer is a prime number, while in one case it is composite. You need to recognise this structure and select the number that does not fit the pattern as the odd one out.

Given Data / Assumptions:

• Numbers: 170, 290, 360 and 530.
• Each number can be written as 10 multiplied by another integer.
• A prime number has exactly two positive divisors.
• Three numbers are of the form 10 * prime, while one is 10 * composite.
• No more complicated operations are required.

Concept / Approach:
Because all four numbers end in zero, we can factor out 10 from each option and inspect the remaining factor. If the remaining factor is a prime number, then the original number can be described as 10 times a prime. The one number whose remaining factor is not prime will be the odd one out. This simple factorisation approach is an efficient way to tackle such questions in competitive exams.

Step-by-Step Solution:
Step 1: Factor 170.170 = 10 * 17. The factor 17 is a prime number.Step 2: Factor 290.290 = 10 * 29. The factor 29 is a prime number.Step 3: Factor 530.530 = 10 * 53. The factor 53 is a prime number.Step 4: Factor 360.360 = 10 * 36. The factor 36 is not prime; it can be written as 6 * 6 or 4 * 9, so it is composite.Step 5: Identify the odd number.Since 170, 290 and 530 are 10 times prime numbers, and 360 is 10 times a composite number, 360 is the odd one out.

Verification / Alternative check:
An alternative check is to perform prime testing directly on the factors. For 17, 29 and 53, none of these factors are divisible by 2, 3 or 5, and their square roots are less than 8, so they can be safely identified as primes. For 36, it is obvious that 36 = 6 * 6, making it composite. This practical test reconfirms that only 360 has a composite factor after removing the common factor 10.

Why Other Options Are Wrong:
170: Equal to 10 * 17, where 17 is prime, so it fits the main pattern.
290: Equal to 10 * 29, where 29 is prime, so it is not the odd one.
530: Equal to 10 * 53, with 53 prime, again matching the pattern.

Common Pitfalls:
Some students might look for patterns in the sum of digits or differences between the numbers instead of checking factors. While such patterns sometimes exist, the cleanest and most reliable pattern here is the prime factor structure. Always try simple factorisation or divisibility rules first when dealing with numbers ending in zero or five, as it often reveals the intended logic quickly.

Final Answer:
The odd number is 360, because 170, 290 and 530 are 10 times prime numbers, whereas 360 is 10 times the composite number 36.