Find the number of positive integers that divide (10)^999 but not (10)^998.

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.