Smallest Number with 28 Positive Divisors

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SUMMARY

The smallest number with 28 positive divisors is determined by analyzing its prime factorization. The divisor count formula indicates that 28 can be expressed as 14*2 or 7*4. This leads to two potential forms: 2^13*3 or 2^6*3^3. The latter, 2^6*3^3, yields a smaller result than the former, confirming it as the correct solution.

PREREQUISITES
  • Understanding of prime factorization
  • Familiarity with divisor count formulas
  • Basic knowledge of exponentiation
  • Ability to compare numerical values
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  • Study the divisor function in number theory
  • Explore prime factorization techniques
  • Learn about the properties of exponents
  • Investigate other numbers with specific divisor counts
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ehrenfest
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Homework Statement


Find the smallest number with 28 positive divisors.

28 = 14*2 or 7*4.

So, it is either 2^13*3 or 2^6*3^3, right?

Because 2^7 is manifestly larger than 3^2, it the latter, correct?

Homework Equations


The Attempt at a Solution

 
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