Divisibility  
 
Introduction  
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There is a great deal of value in developing number sense. Number sense is knowing how to mentally add, subtract, multiply, divide, factor, estimate calculations, ... Knowing how to do those things makes it easier to perform a multitude of duties, like as simple as give change to as complicated as perform several mental calculations to decide if a business transaction is immediately beneficial  and consequently seize an opportunity as it presents itself.
The sections that follow will explore one type of number sense: divisibility. You will learn how to determine if a number is divisible by another number.
 
Numbers that are even are divisible by the number two. Even numbers end in either 2, 4, 6, 8, or 0.
Example:
Example:
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Division by three is accomplished by adding the digits of a number. If the sum of the digits is equal to a number that is a multiple of three, then the original number is divisible by three.
Example: 5 + 0 + 1 = 6. Since 6 is divisible by three, so is 501.
Example: 1 + 4 + 9 + 0 + 2 = 16. Since 16 is not divisible by three, 14902 is not divisible by three.
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Checking for divisibility by five can be done by looking at the last digit of a number. If the digit is either 0 or 5, then it is divisible by 5.
Example:
Example:
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To determine if a number is divisible by six, we have to perform two divisibility checks. Since six has the factors two and three (6 = 2 times 3), all numbers that are divisible by six are also divisible by both two and three.
Example: 2 + 1 = 3. 3 is certainly divisible by three; so, 21 is divisible by three. However, 21 is an odd number because it ends with the number 1. It is not divisible by two. Therefore, 21 is not divisible by six because it is not divisible by both two and three.
Example: 8 + 6 + 1 + 6 = 21. Since 21 is divisible by three, the original number is divisible by three. 8616 is divisible by both two and three. So, it is divisible by six.
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The test for divisibility by nine is similar to that of the division by three check. We have to add the digits and look at this sum to see if it is divisible by nine. If the sum is divisible by nine, so is the number we started with.
Example: 1 + 0 + 5 + 8 + 3 = 17. However, 17 is not divisible by nine. So, 10583 is not divisible by nine.
Example: 4 + 4 + 2 + 1 + 7 = 18. Since 18 is divisible by nine, 44217 is divisible by nine.
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This is a pretty simple test. All numbers that end in 0 are divisible by ten. All one has to do is look at the last digit to determine if the number is divisible by 10.
Example:
Example:
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uiz: Divisibility Check

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