Find the total number of odd divisors of P = 540.1. 242. 213. 204. 23

1.	Find the total number of odd divisors of P = 540.1. 242. 213. 204. 23
Answer» Correct Answer - Option 2 : 21 Given: P = 540 Concept Used: x = a^p × b^q Total number of divisors = (p + 1) × (q + 1) where, a and b → Prime numbers. Total number of divisors = Odd divisors + Even divisors Calculations: P = 540 ⇒ P = 2² × 3³ × 5¹ ⇒ Total number of divisors = (2 + 1) × (3 + 1) × (1 + 1) ⇒ Total number of divisors = 3 × 4 × 2 ⇒ Total number of divisors = 24 Even divisors = (2 + 1) = 3 Total number of divisors = Odd divisors + Even divisors ⇒ Odd divisors = Total number of divisors - Even divisors ⇒ Odd divisors = 24 - 3 ⇒ Odd diviors = 21 ∴ The total number of odd divisors is 21.

Answer» Correct Answer - Option 2 : 21

Given:

P = 540

Concept Used:

x = a^p × b^q

Total number of divisors = (p + 1) × (q + 1)

where, a and b → Prime numbers.

Total number of divisors = Odd divisors + Even divisors

Calculations:

P = 540

⇒ P = 2² × 3³ × 5¹

⇒ Total number of divisors = (2 + 1) × (3 + 1) × (1 + 1)

⇒ Total number of divisors = 3 × 4 × 2

⇒ Total number of divisors = 24

Even divisors = (2 + 1) = 3

Total number of divisors = Odd divisors + Even divisors

⇒ Odd divisors = Total number of divisors - Even divisors

⇒ Odd divisors = 24 - 3

⇒ Odd diviors = 21

∴ The total number of odd divisors is 21.

Discussion

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