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DIVISIBILITY

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The concepts for this exercise are summarized below; for a complete discussion, read the text.

The numbers 0, 2, 4, 6, … are called even numbers.
Even numbers always end in 0, 2, 4, 6, or 8.
Even numbers can always be divided into two equal (even) piles.
Note: The numbers 1, 3, 5, 7, … are called odd numbers.

The numbers 0, 2, 4, 6, … are also said to be divisible by 2.
Divisible by 2 means that 2 goes into the number evenly.
The phrases   even   and   divisible by 2   are interchangeable.

Divisible by 3 means that 3 goes into the number evenly.
Divisible by 4 means that 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.

DIVISIBILITY BY 2
If a number ends in 0, 2, 4, 6, or 8, then the number is divisible by 2.
Also, if a number is divisible by 2, then it ends in 0, 2, 4, 6, or 8.

For example,  87,356  is divisible by 2, since it ends in the digit 6.
However,  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:
Is  57,394  divisible by 3? (Answer without using your calculator!)
Add up the digits in the number: 5 + 7 + 3 + 9 + 4 = 28 .
Add up the digits again: 2 + 8 = 10 .
Since 10 is not divisible by 3, the original number  57,394  is also not divisible by 3.

DIVISIBILITY BY 3
To decide if a number is divisible by 3, add up the digits in the number.
Continue this process of adding the digits until you get a manageable number.
(If you want, keep going until you get a single-digit number.)
If this final number is divisible by 3, then the number you started with is also divisible by 3.
If this final number is not divisible by 3, then the number you started with is not divisible by 3.

Read the text for a proof of the "divisibility by 3" test.

DIVISIBILITY BY 5
If a number ends in 0 or 5, then the number is divisible by 5.
Also, if a number is divisible by 5, then it ends in 0 or 5.

Read the text for a clever "finger trick" for divisibility by 9.

DIVISIBILITY BY 10
If a number ends in 0, then the number is divisible by 10.
Also, if a number is divisible by 10, then it ends in 0.

More compactly, we can say that a number is divisible by  10  if and only if it ends with a  0 .


WEB EXERCISES:
Decide if the number is divisible by 2, 3, 5, and 10.
Check all appropriate boxes.

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2 3 5 10





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When you "end timing," you'll get a summary sheet of your results. Good luck!
     


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CONCEPT QUESTIONS EXERCISE:
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.

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One Mathematical Cat, Please! A First Course in Algebra
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