Looking at each number, let's examine their prime factorizations:
175=52×7=25×7
Prime factors: 5, 7 (both single-digit primes)
137 is a prime number.
To verify: 137≈11.7
Checking divisibility by primes up to 11: not divisible by 2, 3, 5, 7, or 11.
Therefore, 137 is prime (can be considered as having itself as the only prime factor).
247=13×19
Prime factors: 13, 19 (both double-digit primes)
213=3×71
Prime factors: 3, 71 (one single-digit prime)
The pattern:
175: Contains single-digit prime factor (5, 7)
137: Prime number itself (single-digit prime when considering it has only itself)
213: Contains single-digit prime factor (3)
247: All prime factors are double-digit (13 and 19)
Therefore, 247 is the odd one out as it is the only number whose prime factorization contains exclusively double-digit primes.