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What is the smallest positive five-digit integer, with all different digits, that is divisible by each of its non-zero digits? (The number itself may have 0 as a digit.)

 Jul 7, 2015

Best Answer 

 #1
avatar+129852 
+5

Assuming that "0' can only be used once, let's guess that smallest 5 digit number would have to have 102 as its first three digits.

 

Assume that the nexrt digit might be "3"......the following digit can't be 1,2, 3.....it also can't be 4 because 10234 isn't divisible by 3 or 4....and it can't be 10235 because that isn't divisible by 2.or 3.

 

But, 10236  is divisible by all its non-zero digits.

 

 

 Jul 7, 2015
 #1
avatar+129852 
+5
Best Answer

Assuming that "0' can only be used once, let's guess that smallest 5 digit number would have to have 102 as its first three digits.

 

Assume that the nexrt digit might be "3"......the following digit can't be 1,2, 3.....it also can't be 4 because 10234 isn't divisible by 3 or 4....and it can't be 10235 because that isn't divisible by 2.or 3.

 

But, 10236  is divisible by all its non-zero digits.

 

 

CPhill Jul 7, 2015

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