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a)A certain positive integer has exactly 20 positive divisors.

What is the smallest number of primes that could divide the integer?

 

b)A certain positive integer has exactly 20 positive divisors.

What is the largest number of primes that could divide the integer?

 Aug 3, 2020

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240 = (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240) > 20 (divisors)
240 = 2^4 * 3 * 5 - 3 distinct primes - the smallest number.

240 =2 x 2 x 2 x 2 x 3 x 5 - 6 primes - 2 distinct and 4 non-distinct - the largest number.

 Aug 3, 2020

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