In this section, you will learn how to graph conic sections. Here is a list of the sections within this webpage:

• Divisibility Rationale
• Division by Two
• Division by Three
• Division by Five
• Division by Six
• Division by Nine
• Division by Ten
• Interactive Quizzes
• Related Lessons

     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:
For instance, 24 is an even number and it's divisible by two. This is easily known because 24 ends in the number 4.

Example:
3115 is not an even number. It ends in 5, which mean it is not divisible by two.

      uiz: Divisibility Check

     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:
Let us determine if the number 501 is divisible by three. To do so, we need to add the digits, like so.

5 + 0 + 1 = 6. Since 6 is divisible by three, so is 501.

Example:
Is 14902 divisible by three? Let's add the digits to decide.

1 + 4 + 9 + 0 + 2 = 16. Since 16 is not divisible by three, 14902 is not divisible by three.

      uiz: Divisibility Check

     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:
60309 may be a large number, but we only need to look at the 9 to decide if it is divisible by five. Since it is not 0 nor 5, 60309 is not divisible by five.

Example:
Is 42270 divisible by five? Yes, because the number ends in 0.

      uiz: Divisibility Check

     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:
Decide if 21 is divisible by 6. The divisibility by three rule says we need to add the digits.

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:
8616 is an even number because it ends with the number 6. It's divisible by two. To see if it is divisible by three, we have to add all the digits.

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:
Is 10583 divisible by nine? Let's add the digits.

1 + 0 + 5 + 8 + 3 = 17. However, 17 is not divisible by nine. So, 10583 is not divisible by nine.

Example:
44217 is a big number, but let's add the digits.

4 + 4 + 2 + 1 + 7 = 18. Since 18 is divisible by nine, 44217 is divisible by nine.

      uiz: Divisibility Check

     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:
3000001 has a great deal of 0s digits. However, it's last digit is 1. Since that last digit is not 0, 3000001 is not divisible by 10.

Example:
670 ends with the number 0. So, 670 is divisible by ten.

      uiz: Divisibility Check

    After reading the lessons, try our quizmaster.

      uiz: Divisibility Check

    Here are related lessons to view.

      esson: Operations on Integers