Answer :

Given, A679B a number.

Need to find out it is divisible by 72.


Prime factors of 72 = 9 and 8


So, it is enough to check the given 5-digit number is divisible by 9 and 8.


To check the number is divisible by 8 last three digits must be divisible by 8.


79B is divisible by 8 should be checked.


Now, from divisibility rule 100b + 10c + d


We get


100(7) + 10(9) + B = 790 + B


Substitute a number in B which satisfy the equation using trail error method


B must be 2 to be divisible by 8


792 is divisible by 8


A679B = A6792 is divisible by 8


A6792 is divisible by 9 only if sum of the given digits is divisible by 9


A + 6 + 7 + 9 + 2 = A + 24


Put a value in A which satisfy the equation


A = 3


A + 24 = 27 is divisible by 9.


A679B is divisible by 72 and the values of A = 3 and B = 2


Hence, 36792 is divisible by 72


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