120 Prime Factorization
First, find the prime factorization of the number 120.
$120 = 2^3 \\times 3^1 \\times 5^1$
Total Divisors Calculation
The total number of divisors is calculated by adding 1 to each exponent in the prime factorization and multiplying the results.
Number of divisors = $(3+1) \\times (1+1) \\times (1+1) = 4 \\times 2 \\times 2 = 16$
Odd Divisors Count
To find the number of odd divisors, consider only the odd prime factors (3 and 5). The power of 2 is excluded.
Number of odd divisors = $(1+1) \\times (1+1) = 2 \\times 2 = 4$
Even Divisors Count
The number of even divisors is the total number of divisors minus the number of odd divisors.
Number of even divisors = Total divisors - Odd divisors
Number of even divisors = $16 - 4 = 12$
Final Answer Derivation
The number of odd divisors is 4, and the number of even divisors is 12.
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