1's and 0's and 225
Number Theory
Level
1
Find the smallest positive base-10 integer composed entirely of 1's and 0's that is divisible by 225.
The answer is 11111111100.
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1 solution
225 = 9 * 25
Numbers divisible by 25 end in 25, 50, 75 or 00. So our number must end in 00.
Numbers divisible by 9 have a digital root divisible by 9. So our number must have 9 1's in it.
Therefore, the number in question is 9 1's followed by 00, or 11,111,111,100.