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Are all numbers divisible by 9 also divisible by 3?

 Jun 21, 2017
 #1
avatar+27902 
+3

Yes.

 

If integer n is exactly divisible by 9 then it can be expressed as n = 9*m where m is another integer.

 

This means that n/3 = 9*m/3 → 3*m, an integer.

 

.

 Jun 21, 2017
 #2
avatar+101733 
+2

The short answer is yes

 

Take any number, say 36

Work out the prime facrtors of 36

9*4=39

3*3*2*2=36

 

any number that you can get bu multiplying any of thes prime factors together will also be a factor of 36..

 

so

2

3

2*2

2*3

2*2*3

3*3

3*2*2

3*3*2

3*3*2*2

 Jun 21, 2017

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