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Find the number of positive integers which divide 100^999 but not 100^998

Find the number of positive integers which divide 100^999 but not 100^998

Grade:12

2 Answers

Arun
25750 Points
5 years ago
Let d(n) be the number of positive integers that divide n. 
The following statements are true. 
1. If GCD(m,n) = 1, then d(m n) = d(m) d(n). 
2. If p is a prime number, then d(p^n) = n+1 

So you want to compute 
d(10^999) - d(10^998) = 
d(2^999) d(5^999) - d(2^998) d(5^998) = 
1000^2 - 999^2 = 
(1000 - 999) (1000 + 999) = 
1999
Aman
13 Points
one year ago
Let d(n) be the number of positive integers that divide n. 
The following statements are true. 
1. If GCD(m,n) = 1, then d(m n) = d(m) d(n). 
2. If p is a prime number, then d(p^n) = n+1 
 
So you want to compute 
d(10^999) - d(10^998) = 
d(2^999) d(5^999) - d(2^998) d(5^998) = 
1000^2 - 999^2 = 
(1000 - 999) (1000 + 999) = 
1999
 

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