Which among the choices contains the highest number of integer divisors?
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Answer: C. 176
Explanation
Prime factorization yields distinct prime powers that determine the total number of integer divisors. Adding one to each exponent and multiplying the results together gives the divisor count. For 176, the calculation produces ten divisors, which is higher than the other choices. Integer divisors are whole numbers that divide evenly into another integer without leaving any remainder. Prime factorization breaks any composite integer down into a unique product of prime numbers. Multiplying the incremented exponents of these prime factors is a standard combinatorial formula.
Understanding divisor counts is useful in cryptography, number theory, and algorithm optimization tasks. Engineers and mathematicians use factor properties to analyze periodic structures and harmonic frequencies. Comparing divisor quantities helps identify highly composite numbers with special mathematical properties. Number 99 factors into three squared times eleven, yielding only six total integer divisors. Number 101 is a prime number, which means it only possesses two integer divisors total. Number 182 factors into two, seven, and thirteen, resulting in exactly eight integer divisors.
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