The numbers
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$0$, $2$, $4$, $6$, … are called even numbers.
Even numbers always end in one of these digits: $0$, $2$, $4$, $6$, or
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$\,8\,$.
Even numbers can always be divided into two equal (even) piles.
Note: The numbers
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$1$, $3$, $5$, $7$, … are called odd numbers.
The numbers
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$0$, $2$, $4$, $6$, … are also said to be divisible by 2.
Divisible by 2 means that
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$\,2\,$ goes into the number evenly.
The phrases even and divisible by 2 are interchangeable.
Divisible by 3 means that
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$\,3\,$ goes into the number evenly.
Divisible by 4 means that
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$\,4\,$ goes into the number evenly; and so on.
A divisibility test is a shortcut to decide if a number is divisible by a given number.
For example,
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$\,87{,}356\,$ is divisible by $\,2\,$, since it ends in the digit $\,6\,$.
However,
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$\,87{,}357\,$ is not divisible by $\,2\,$, since it ends in the digit $\,7\,$.
There's a neat trick for deciding if a number is divisible by $\,3\,$.
The technique is illustrated with the following example:
☆ (speed-it-up trick!)
Let's re-do the previous example, being a bit more clever.
You don't really have to add up all the digits!
Looking at the number $\,57{,}394\,$, the digits $\,3\,$ and $\,9\,$ are clearly divisible by $\,3\,$.
So, don't bother including them in your sum!
That leaves you with $\,5\,$, $\,7\,$ and $\,4\,$.
But, the sum of $\,5\,$ and $\,7\,$ is $\,12\,$, which is divisible by $\,3\,$.
So, you're really only left with the digit $\,4\,$, which is clearly not divisible by $\,3\,$.
If you get into the habit of discarding $\,3\,$'s, $\,9\,$'s, and obvious sums that give a multiple of $\,3\,$ (like $\,5 + 7\,$), then this test can go much faster!
Read the text for a proof of the "divisibility by 3" test (on page 14).
Read the text for a clever "finger trick" for divisibility by 9 (on page 15).
More compactly, we can say that a number is divisible by 10 if and only if it ends with a 0.