If $a$ is a positive integer and $81$ divided by $a$ results in a remainder of $1,$ what is the value of $a?$

If $a$ is a positive integer and $81$ divided by $a$ results in a remainder of $1,$ what is the value of $a?$

(1) The remainder when a is divided by $40$ is $0.$
(2) The remainder when $40$ is divided by a is $40.$

Answer: B

Source: Manhattan GMAT

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