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# Digit problem

0
67
2

The five-digit number $\overline{a679b}$ is divisible by 72. Find the digits a and b.

Jul 22, 2021

#1
+74
+1

a=3 b=2

Jul 22, 2021
#2
+18
0

Thanks Wsai, here is another way to do it

Divisibility rule for 72 : Divisible by 8 and 9

$$\overline{a679b}$$ = 10000a+6000+700+90+b

so we have two equations:

(790+b)/8 is an integer

a + 6+7+9+b is divisible by 9

so a=3 and b=2

Check

(790+2)/8 = 99 :)

(3 + 6  + 7 + 9 + 2)/9 = 3:)

Jul 22, 2021