Question

The number of divisors of 360 (excluding 1 and 360) is:

• A. 22
• B. 24
• C. 20
• D. 18

Hint:

Always check if the question asks for "proper divisors" or excludes specific ones like 1 and the number itself.

Answer 1

The Correct Option is A

Step 1: Concept
If $N = p_1^{a} p_2^{b} \dots$, total divisors $= (a+1)(b+1)\dots$.
Step 2: Analysis
$360 = 2^3 \times 3^2 \times 5^1$.
Total divisors $= (3+1)(2+1)(1+1) = 4 \times 3 \times 2 = 24$.
Step 3: Conclusion
Excluding 1 and 360, the number of divisors is $24 - 2 = 22$.
Final Answer: (A)