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# Divisibility Rules

By the time they reach grade 5, math students are beginning to understand that they can sometimes get to their final answer in different ways. Now, we all know that in math there is one correct answer and, generally speaking, one correct method of arriving at that answer.

Even when following the prescribed protocol and steps to get the correct answer, children can utilize their memory and particular memory aids to help them get there faster. After all, if they can get to one answer quicker, they are generating extra time to help them find some of the trickier questions on the test, or in the math competition they’re participating in.

One way of speeding up their mathematical processes is for children to understand divisibility rules for various numbers, and to recognize an opportunity to apply one of these rules.

## Recognizing Divisibility

First things first, let’s take a step back and make sure we are all on the same page about divisibility, what it means, and how to recognize some of the different rules.

One number is divisible by another if, when you divide the first number by the second number, your answer is a whole number.

Another way to say “divisible by” is to say “can be exactly divided by”. Let’s look at some examples.

16 is divisible by 4 because the answer is 4, and, as we know, 4 is a whole number.

17 is not divisible by 4 because the answer is 4/17, which is not a whole number.

As you practice these types of problems more and more, you will find it easier to recognize quicker and quicker which numbers are divisible by 2, 3, 4, and any other number. Here is a great educational video explaining how you can learn to recognize divisibility in more complex problems faster.

## Rules of Divisibility

As we’ve seen, the rules of divisibility can help children calculate much more quickly, but they must be able to identify these “shortcuts” to take advantage of them. Let’s look at some of the rules of divisibility now, and see which ones are easy and which ones will require a little more thought and practice.

Any integer (whole number, not a fraction) is divisible by 1.

Any number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.

Any number is divisible by 3 if the sum of the digits is divisible by 3.

For example:

• 381 (3+8+1=12, and 12÷3 = 4) Yes, this is divisible by 3
• 217 (2+1+7=10, and 10÷3 = 3 1/3) No, this is not divisible by 3

Any number is divisible by 4 if the last two digits are divisible by 4.

Any number is divisible by 5 if the final digit is a 5 or a 0.

Any number is divisible by 10 if it ends in a 0.

These are some of the most famous, and straightforward, divisibility rules that middle schoolers will have to become familiar with. Next, let’s take a look at some of the more challenging divisibility rules, along with some examples to show that, although they are a bit tougher, they can also be recognized and used to calculate quickly.

Any number is divisible by 6 if it satisfies both rules of divisibility for 2 & 3.

In other words, a number is divisible by 6 if it ends in 0, 2, 4, 6, or 8 AND the sum of its digits is divisible by 3.

For example:

• Is 72 divisible by 6?
• 7+2 = 9 = 3, so it satisfies rule 3
• 72 ends in a 2, so it satisfies rule 2
• Therefore, we know 72 is divisible by 6

Any number divisible by 12 if it satisfies rules 3 & 4 above.

In other words, a number is divisible by 12 if the sum of its digits is divisible by 3 AND the last two digits are divisible by 4.

For example:

• Is 108 divisible by 12?
• 1+0+8 = 9, 9 is divisible by 3, so it satisfies rule 3
• 08 = 8, 8 is divisible by 4, so it satisfies rule 4

As you can see there are a whole host of these tricks that can be learned and, if learned properly, they can generate a fantastic advantage for kids in math class. As always, practice makes perfect!

## At OMC

Grade 5 is when math students begin to understand the subject and, when studying under the right conditions, they begin to see their progress accelerate rapidly. Individual math tutoring has provided a wide variety of students of all ages and levels with an opportunity to plug gaps in their knowledge, focus on topics in more detail with more attention, and ultimately improve their performance in math class throughout middle school and high school.

Contact OMC today and enroll your child in our middle school math course, or take a look at the other options available for children of all ages, from SAT preparation courses, to practice for math competitions.

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