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Explain why any number that is divisible by 9 is also divisible by 3.

Explain why any number that is divisible by 9 is also divisible by 3.

 

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1 Answer

Since 9 = 3 * 3, 9 is divisible by 3. By extension, 3 would be a factor of any number divisible by 9.

Let's look at an example - say, 72. 

We know that 9 * 8 = 72. Now, since 9 = 3*3, we can replace 9 in our example to get 3*3*8 = 72, which shows that 72 is divisible by both 9 and 3. 

Comments

Also a neat little trick is if the digits add up to a number divisible by 3 then the number is divisible by 3.  EX: 7+2=9 so 72 is divisible by 3. or 15 1+5=6 so 15 is divisible by 3.  This little trick will help you when you need to factor numbers.