What is the total number of odd and even divisors of 120, respectively?

Correct option is B

​Given:

Number = $$120$$​​

Formula used :

Total divisors:

​$$\text{Total Divisors} = (e_1 + 1)(e_2 + 1)(e_3 + 1)$$

where $$e_1, e_2 \ and \ e_3$$​ are the powers of the prime factors

Solution:

Prime Factorization = $$120 = 2^3 \times 3^1 \times 5^1$$​​

​Odd divisors: Only from odd prime factors:

(1 + 1)(1 + 1) = 4

Even divisors:

​$$\text{Total Divisors} - \text{Odd Divisors}$$​​

$$\text{Total Divisors} = (3 + 1)(1 + 1)(1 + 1) = 16$$​​

Odd Divisors = 4

Even Divisors = 16 − 4 = 12