How many natural divisors does 121 have? How many natural divisors does 1000 have? How many natural divisors does 1000000000 have?
$121=11^{2}$. Therefore, the natural divisors of 121 are exactly 1, which has no prime factors, and the naturals for which 11 is the only prime factor and this prime factor appears 1 or 2 times in the prime factorization, which are 11 and 121. Thus, 121 has exactly 3 natural divisors.

$1000=2^{3} \cdot 5^{3}$. The natural divisors of 1000 are therefore exactly the naturals with only 2 and 5 in the prime factorization and which have 0, 1, 2, or 3 times 2 and 0, 1, 2, or 3 times 5. There are four possibilities for how many factors of 2 there are and four possibilities for how many factors of 5 there are, which gives a total of $4 \cdot 4=16$ divisors.

$1000000000=2^{9} \cdot 5^{9}$. Therefore, similarly to the previous question, it has $(9+1) \cdot (9+1)=$ 100 divisors.