# The six-digit number A4273B is divisible by 72 without a remainder. Find the values of A and B.

2
by Jewellalysa

2015-09-26T08:48:37+08:00
A: 5
B: 6

542, 736 / 72
is 7538
∵No remainders
∵Matching Digits
2015-09-26T13:35:36+08:00

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Since it is divisible by 72, it should be divisible by 9 and 8.

In order for the number to be divisible by 9, it should have digits with a sum which is a multiple of 9. So,

A + 4 + 2 + 7 + 3 + B = A + B + 16, this is divisible by 9.

For the number to be divisible by 8, the last 3 digits must be divisible by 8.

73B is divisible by 8 therefore 73B  is 736.

B = 6

A + B + 16 = A + 6 + 16 = A + 22 is divisible by 9 therefore A + 22 = 27 so A = 5.

Therefore A = 5 and B = 6.