If a is the number of all even divisors and b | vedclass

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(B) The given number is $10800$. Prime factorization of $10800$ is $2^4 	imes 3^3 	imes 5^2$. The total number of divisors is $(4+1)(3+1)(2+1) = 5 \

Vedclass · Accepted Answer

$132$

Vedclass · Answer

(B) The given number is $10800$. Prime factorization of $10800$ is $2^4 	imes 3^3 	imes 5^2$. The total number of divisors is $(4+1)(3+1)(2+1) = 5 	imes 4 	imes 3 = 60$. The number of odd divisors is found by considering only the odd prime factors: $(3+1)(2+1) = 4 	imes 3 = 12$. Thus,$b = 12$. The number of even divisors is the total number of divisors minus the number of odd divisors: $a = 60 - 12 = 48$. Therefore,$2a + 3b = 2(48) + 3(12) = 96 + 36 = 132$.

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

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