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What is the least positive integer multiple of 30 that can be written with only the digits 0 and 2?

 May 22, 2020
 #1
avatar+675 
+3

25!=1*2*3*4*5*6*...23*24*25

26= 2*13
28=2*14or 4*7
36=2*18or 3*12 or 4*9
56=7*8
All products above are inside 25! So they are all factors of 25!
But 58=2*29 and 29 is not inside 25! so it's not a factor of 25!

 

Hope this helps, whymenotsmart^m^.

 
 May 22, 2020
 #2
avatar+30028 
+2

"What is the least positive integer multiple of 30 that can be written with only the digits 0 and 2?"

 

Must begin with 2 and end with 0.  The sum of the digits must be divisible by 3.  The smallest therefore seems to be 2220  (which is 74*30).

 
 May 22, 2020

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