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Josef and Timothy play a game in which Josef picks an integer between 1 and 1000 inclusive and Timothy divides 1000 by that integer and states whether or not the quotient is an integer. How many integers could Josef pick such that Timothy's quotient is an integer?

 Mar 19, 2019
 #1
avatar+929 
+2

You can just count the number of factors of 1000, which is 4x4=16.

 Mar 19, 2019
 #2
avatar+140 
+1

thanks

CorbellaB.15  Mar 19, 2019
 #3
avatar+978 
-1

There are 16 because there are 16 divisors of 1000.

 

You are very welcome!

:P

 Mar 19, 2019
 #4
avatar+4330 
+2

Break 1000 into its prime factorization: 2^3*5^2, so 4*4=16 factors. (add one to each power, then multiply) 

 Mar 19, 2019

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