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Both b and n are positive integers less than or equal to 15. What is the greatest number of positive factors b*n can have?

 
 Nov 22, 2020
 #1
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10 x 12 = 120 has 16 divisors: (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) >>Total = 16 divisors

Also:

12 x 14 =168 has 16 divisors: (1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168) >>Total = 16 divisors

 
 Nov 22, 2020
 #2
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Sorry, misread the question:

 

12 x 14 should be: 12 x 15 =180=  (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180) >>Total = 18 divisors

 
Guest Nov 22, 2020

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