# UKMT Special (Problem $15$)

The five-digit number $a679b$ is a multiple of $72$

What are the values of $a$ and $b$?

[UKMT Hamilton Olympiad $2015$, H$1$]

Note by Yajat Shamji
8 months, 2 weeks ago

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- 8 months, 2 weeks ago

Step 1) A number is divisible by 72, if and only if it is divisible by 8 and 9.

Step 2) According to divisibility rules, a679b is divisible by 8 if 79b is divisible by 8.

   Only b = 2 that satisfy.


Step 3) According to divisibility rules, a6792 is divisible by 8 if a + 6 + 7 + 9 + 2 is divisible by 9.

   a + 6 + 7 + 9 + 2 = a + 24 is divisible by 9.
Only a = 3 that satisfy


The five-digit number is 36792.

- 8 months, 2 weeks ago

Correct solution and method!

- 8 months, 2 weeks ago