If a is the number of all even divisors and b is the number of all odd divisors of the number 10800 , then 2 a + 3 b =

Step-by-step solution

Given number is 10800 Prime factorisation of 10800 is 2 4 × 3 3 × 5 2 The total number of divisors = 4 + 1 3 + 1 2 + 1 = 5 4 3 = 60 The number of odd divisors = 1 3 + 1 2 + 1 = 1 4 3 = 12 The number of even divisors = 60 - 12 = 48 Here., a = 48 ,   b = 12 ⇒ 2 a + 3 b = 2 48 + 3 12 = 96 + 36 ∴   2 a + 3 b = 132