Final answer:
The natural number divisors of 330 are found by factoring 330 into prime factors and listing all the combinations, which results in 16 divisors including 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, and 330.
Step-by-step explanation:
To determine all natural numbers that are divisors of 330, we first factorize 330 into its prime factors. The prime factorization of 330 is 2 x 3 x 5 x 11. Now, we list all combinations of these prime factors to find the divisors.
- 1 (by itself is always a divisor)
- 2 (by itself is always a divisor)
- 3 (by itself is always a divisor)
- 5
- 6 (2 x 3)
- 10 (2 x 5)
- 11
- 15 (3 x 5)
- 22 (2 x 11)
- 30 (2 x 3 x 5)
- 33 (3 x 11)
- 55 (5 x 11)
- 66 (2 x 3 x 11)
- 110 (2 x 5 x 11)
- 165 (3 x 5 x 11)
- 330 (2 x 3 x 5 x 11)
So, the natural number divisors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, and 330.