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Find a five-digit multiple of 12 that uses only the digits 0 and 1.

Dabae  Jul 7, 2015

Best Answer 

 #1
avatar+17746 
+10

Any 5-digit multiply of 12 must be at least 10000.

Because 12 is 4 x 3, any multiply of 12 must be divisible by both 3 and 4.

To be a multiply of 3, the sum of the digits must be divisible by 3.

Since the only digits are either 1 or 0, the number must contain three 1s.

To be divisible by 4, the number must be even, so it must end with a zero; and, since its "twice-even", it must end with two 0s.

11100 fills the requirements...

geno3141  Jul 7, 2015
 #1
avatar+17746 
+10
Best Answer

Any 5-digit multiply of 12 must be at least 10000.

Because 12 is 4 x 3, any multiply of 12 must be divisible by both 3 and 4.

To be a multiply of 3, the sum of the digits must be divisible by 3.

Since the only digits are either 1 or 0, the number must contain three 1s.

To be divisible by 4, the number must be even, so it must end with a zero; and, since its "twice-even", it must end with two 0s.

11100 fills the requirements...

geno3141  Jul 7, 2015
 #2
avatar+94105 
+5

Thanks Geno.

I like questions like these.  

Many people are capable of trying them , if they are patient enough then they can probably get an answer by themselves, but if they look at your answer as well then they could learn a lot.    

These questions are great for gaining understanding of how numbers 'work'.

Melody  Jul 11, 2015

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