To find the number of divisors of 30, we first find the prime factorization of 30.
\( 30 = 2 \times 3 \times 5 \)
The prime factorization has three distinct prime factors, each raised to the power of 1.
To find the total number of divisors, we add 1 to each exponent and multiply the results:
Number of divisors = \( (1+1) \times (1+1) \times (1+1) = 2 \times 2 \times 2 = 8 \)
The divisors of 30 are: 1, 2, 3, 5, 6 (2×3), 10 (2×5), 15 (3×5), and 30 (2×3×5).
Ответ: 8