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A certain positive integer has exactly 20 positive divisors.

 

What is the smallest possible value of the number?

What is the largeest possible value of the number?

 Feb 3, 2021
 #1
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This has been asked before

 

a)  We could have two primes that divide the integer 

Suppose that the number can be prime-factored into  a^m * b^n

So

(m + 1) ( n + 1)  =  20

And  m, n    could be  (in some order)   

3, 4  or

1, 9

 

b )   We could have three primes that divide the integer

Suppose that the integer  can be prime-factored into  a^k * b *m * c ^n

So

(k + 1) (m + 1) ( n + 1)  = 20

And k, m, n   could be  (in some order)

1, 1, 4

 

Credit to CPhill for answer

 Feb 3, 2021
 #2
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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)

 Feb 3, 2021

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