The number of odd positive divisors of 67500 | vedclass

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Question

(C) First,find the prime factorization of $67500$: $67500 = 675 	imes 100 = (25 	imes 27) 	imes (4 	imes 25) = 5^2 	imes 3^3 	imes 2^2 	imes 5^

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) First,find the prime factorization of $67500$: $67500 = 675 	imes 100 = (25 	imes 27) 	imes (4 	imes 25) = 5^2 	imes 3^3 	imes 2^2 	imes 5^2 = 2^2 	imes 3^3 	imes 5^4$. To find the number of odd positive divisors,we consider only the odd prime factors,which are $3$ and $5$. The odd divisors are of the form $3^a 	imes 5^b$,where $0 \le a \le 3$ and $0 \le b \le 4$. The number of choices for $a$ is $(3+1) = 4$. The number of choices for $b$ is $(4+1) = 5$. Therefore,the total number of odd positive divisors is $4 	imes 5 = 20$.

The number of odd positive divisors of $67500$ is

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