Which among the options possesses the greatest quantity of divisors?
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Answer: C. 176
Explanation
Prime factorizing each candidate number reveals the exact exponents required to calculate total divisors. The number one hundred seventy-six factors into two to the fourth power multiplied by eleven to the first. Adding one to each prime exponent and multiplying gives five times two, yielding ten total divisors. Divisor counting formulas require expressing integers as products of unique prime number factors raised to powers. Incrementing each prime factor exponent by one and finding their product determines the divisor count. Comparing divisor quantities across multiple integers identifies which number possesses the greatest set of factors.
Number theory researchers analyze divisor functions extensively to understand arithmetic properties of integers. Cryptography algorithms utilize prime factorization complexities to secure digital data transmission across networks. Music theorists study mathematical divisor ratios to understand harmonic frequency intervals in acoustic tuning systems. Option A suggests ninety-nine whose prime factorization yields fewer total divisors than one hundred seventy-six. Option B proposes one hundred one which is a prime number possessing only two total divisors. Option D implies one hundred eighty-two which factors into fewer combinations than the correct choice.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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