If a679b is a five digit number in base 10 and is divisible by 72, then what are the values of a and b

Please support your answer with an explanation

72 = 2^3 * 3^2 = 8*9
a679b is divisible by 8 when 79b is divisible by 8
b must be 2
a679b = a6792
a6792 is divisible by 9 when sum of the digits is divisible by 9
(24+a) must be a multiple of 9
24+a = 27
a = 3
36792 .....answer

Well, we know that the five digit number will be divisible by 9 and by 8, and that will narrow things down. If the sum of the digits of a number are divisible by 9, then the entire number will be divisible by 9, so we know that (a + 6 + 7 + 9 + b) = (a + b + 22) will be divisible by 9.
Also, since 1000 is divisible by 8, a number will be divisible by 8 if the lowest three digits are divisible by 8. In the range 790-799, the only one that is divisible by 8 is 792, so we know that b=2.
That means (a + 24) must be divisible by 9, so a must be 3.

3 and 2

72 * 511