Find the value of A if the given no.7A579808 is divisible by 33

Dear student,

Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{It} \mathrm{is} \mathrm{required} \mathrm{to} \mathrm{find} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{A} \mathrm{so} \mathrm{that} 7\mathrm{A}579808 \mathrm{is} \mathrm{divisible} \mathrm{by} 33 \\ \mathrm{Since} \frac{7\mathrm{A}579808}{33}=\frac{7\mathrm{A}579808}{3\times 11} \\ \mathrm{This} \mathrm{implies} \mathrm{that} \mathrm{the} \mathrm{given} \mathrm{number} \mathrm{is} \mathrm{divisible} \mathrm{by} 33 \mathrm{if} \mathrm{it} \mathrm{passes} \mathrm{the} \mathrm{divisiblity} \\ \mathrm{test} \mathrm{for} \mathrm{both} 3 \mathrm{and} 11 \\ \mathrm{A} \mathrm{number} \mathrm{is} \mathrm{divisible} \mathrm{by} 3 \mathrm{if} \mathrm{the} \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{digits} \mathrm{of} \mathrm{a} \mathrm{number} \mathrm{is} \mathrm{divisible} \mathrm{by} 3. \\ \mathrm{A} \mathrm{number} \mathrm{is} \mathrm{divisible} \mathrm{by} 11 \mathrm{if} \mathrm{the} \mathrm{number} \mathrm{obtained} \mathrm{by} \mathrm{alternatively} \mathrm{adding} \mathrm{and} \\ \mathrm{subtracting} \mathrm{all} \mathrm{of} \mathrm{the} \mathrm{digits} \mathrm{of} \mathrm{the} \mathrm{number} \mathrm{is} \mathrm{divisble} \mathrm{by} 11. \\ \mathrm{Now} \mathrm{add} \mathrm{all} \mathrm{the} \mathrm{digits} \mathrm{of} \mathrm{a} \mathrm{number} 7\mathrm{A}579808 \\ 7+\mathrm{A}+5+7+9+8+0+8=44+\mathrm{A} \\ \mathrm{This} \mathrm{number} \mathrm{should} \mathrm{be} \mathrm{divisible} \mathrm{by} 3 \mathrm{so} \mathrm{we} \mathrm{get} \\ 44+\mathrm{A}=3\mathrm{m} \\ \mathrm{Alternatively} \mathrm{add} \mathrm{and} \mathrm{subtact} \mathrm{all} \mathrm{of} \mathrm{the} \mathrm{digits} \mathrm{of} \mathrm{the} \mathrm{number} 7\mathrm{A}579808 \mathrm{to} \mathrm{get}, \\ 7-\mathrm{A}+5-7+9-8+0-8=2-\mathrm{A} \\ \mathrm{This} \mathrm{number} \mathrm{should} \mathrm{be} \mathrm{divisible} \mathrm{by} 11 \mathrm{so} \mathrm{we} \mathrm{get} \\ 2-\mathrm{A}=11\mathrm{n} \\ \mathrm{Note} \mathrm{that} \mathrm{there} \mathrm{does} \mathrm{not} \mathrm{exist} \mathrm{any} \mathrm{value} \mathrm{of} \mathrm{A} , \mathrm{that} \mathrm{is} \mathrm{the} \mathrm{digits} \mathrm{from} 0 \mathrm{to} 9 \mathrm{does} \\ \mathrm{not} \mathrm{satisfy} \mathrm{the} \mathrm{conditions} 44+\mathrm{A}=3\mathrm{m} \mathrm{and} 2-\mathrm{A}=11\mathrm{n} \mathrm{simultaneously}. \\ \mathbf{So}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{number}\mathbf{ }\mathbf{7}\mathbf{A}\mathbf{579808}\mathbf{ }\mathbf{is}\mathbf{ }\mathbf{not}\mathbf{ }\mathbf{divisble}\mathbf{ }\mathbf{by}\mathbf{ }\mathbf{33}\mathbf{ }\mathbf{for}\mathbf{ }\mathbf{any}\mathbf{ }\mathbf{value}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{A}\mathbf{.} \end{gathered}$$

Hope this information will clear your doubts about the topic.

If you have any more doubts, just ask here on the forum and our experts will try to answer it as soon as
possible.

Regards