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How many Integers? (Posted on 2006-05-18) Difficulty: 2 of 5
Find the number of positive integers that divide (10)^999 but not (10)^998.

No Solution Yet Submitted by Ravi Raja    
Rating: 3.0000 (1 votes)

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No Subject | Comment 8 of 9 |

10^999=(2)^999 *(5)^999

one integer that divides 10^999 but not 10^998 is  10^999

also other integers are as follows

first set:->  2^999, 2^999 *5, 2^999 * 5^2, ......., 2^999 * 5^998 so all these are 999 in number

second set:-> 5^999, 5^999 *2, 5^999* 2^2,......,5^999*2^998 all these are 999 in number.

thus total numbers are 999+999+1= 1999 integers.


  Posted by kumar sharma on 2006-05-26 05:44:04
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