To master mathematics, you have to know the rules. The more tools you have in that tool shed, the more likely one will get the job done. Here, we explore divisibility properties for the numbers up to 11. Once you add these properties to your arsenal, you will be that much further along to mastering this most difficult subject.

__ Divisibility Tests for Numbers__:

__ 2__: If the number is even, that is, if the number ends in 0, 2, 4, 6, or 8, then that number is divisible by 2. Thus, 358 and 4,034,032 are divisible by 2.

__ 3__: If the sum of the digits of the number is divisible by 3, then the given number is also. Thus, 324 and 1,345,611 are both divisible by 3 since the sums of their digits, 9 and 21, respectively, are both divisible by 3.

__ 4__: If the last two digits of the number are divisible by 4, then so is the number. Thus, 312 and 1,024 are both divisible by 4.

__ 5__: If the number ends in 0 or 5, then the number is divisible by 5. Thus, 1,000 and 405 are both divisible by 5.

__ 6__: If a number is divisible by both 2 and 3, then the number is divisible by 6. You can test divisibility by 2 and 3 using the tests above. Once this is established, you are certain that the number is divisible by 6. Thus, 312 and 4,002 are both divisible by 6. Another way of saying this is if the number is even and the sum of the digits is divisible by 3, then the number is divisible by 6.

__ 7__: This rule is probably the most labor intensive of all. Yet, this rule works very well, especially when dealing with large numbers. Let us illustrate it with a specific example. Take the number 2,667. To determine whether this number is divisible by 7, we do the following: we take the last digit, namely 7, multiply it by 2 to get 14 and subtract this from the three digits, namely 266, that remain after we remove the 7. Thus 266 – 14 = 252. Repeat the procedure and we have 2×2 = 4; 25 – 4 = 21, and 21 is divisible by 7. Generally, repeat the procedure until you get to a number that is a few multiples of 7, so that you recognize the divisibility by this number.

__ 8__: If the last three digits form a number divisible by 8, then the entire number is divisible by 8. Thus, 4,096 and 1,016 are divisible by 8.

__ 9__: As with 3, if the sum of the digits forms a number divisible by 9, then the number is too. Thus, 108 and 3,240 are divisible by 9.

__ 10__: This is probably the easiest rule. Simply, if the number ends in 0, then it is divisible by 10.

__ 11__: If the alternate sum of the digits results in a number that is divisible by 11, including 0, then the entire number is divisible by 11. For example, take the number 5,082. Perform 5-0+8-2 = 11. Since 11 is divisible by 11, obviously, then the entire number is as well.

Learn these divisibility properties and I guarantee that your knowledge in and ability with mathematics will grow exponentially. For those parents who want their children to perform better in math, then see that your children master these rules. For then, the sky truly will be the limit.

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