 Is 458 divisible by 2? If you divide 458 by 2, will it divide evenly with no remainder? Most people know that the answer is yes. They recognize that even numbers divide by 2. We say that 'Numbers that are even are divisible by 2' ... they divide by 2 with no remainder. A number is even if it ends in 0, 2, 4, 6, or 8. Divisibility Rule for 2: If a number is even (it ends in 0, 2, 4, 6, or 8) then it is divisible by 2 This divisibility rule means that you don't have to check by dividing. You can look at a number, for example 3,690, and know immediately that it will divide by 2, because it ends in 0. Are there other divisibility rules? For example, is there a quick way to know whether 12,492 will divide evenly by 9, without actually dividing? The answer is yes. We're going to look at some common divisibility rules. Divisibility Rule for 3: A number is divisible by 3 if its digits add to something that is divisible by 3 For example, does 7,218 divide exactly by 3? It's too big to tell just by looking, but if we add the digits: 7 + 2 + 1 + 8 we get 18, which we can easily ecognize as being divisible by 3. So 7,218 is divisible by 3. Another example: is 517 divisible by 3? Since the digits add to 13, which doesn't divide by 3, we know that the answer is no 517 is not divisible by 3 Divisibility Rule for 4: A number is divisible by 4 if the last two digits are a number that divides by 4 For example, is 32,736 divisible by 4? Since the last two digits are 36, and 36 divides by 4 (4x9=36), then 32,736 is divisible by 4. Another example: is 173,429 divisible by 4? Since the last two digits are 29, which does not divide exactly by 4, then 173,429 is not divisible by 4. Sometimes this divisibility rule isn't quite so easy to use. For example, look at the number 1,492. The last two digits are 92. Does 92 divide evenly by 4? You might not know. You'll need to use a little logic: count backwards by 4's from 100, which we know divides by 4. We get 100, 96, 92 So 92 is divisible by 4. This means that 1,492 is divisible by 4. Divisibility Rule for 5: A number is divisible by 5 if it ends in a 5 or 0 For example, is 735 divisibe by 5? Yes, because it ends in 5 Another example: is 12,290 divisible by 5? Yes, because it ends in 0. Divisibility Rule for 6: A number is divisible by 6 if it is divisible by 2 and by 3 This means you'll need to check if it's even (divisible by 2) and if the digits add to something that divides by 3 (divisible by 3) Here's an example: Is 6,294 divisible by 6? - Since it's even (ends in 4), 6,294 is divisible by 2 - Since the digits add to 21, which divides evenly by 3, then 6,294 is divisible by 3 Since 6,294 divides by 2 and by 3, then 6,294 is divisible by 6. Another example: is 958 divisible by 6? - 958 is even, so it divides by 2 - The digits add to 22, which doesn't divide by 3, so 958 won't divide by 3 958 is not divisible by 6. Divisibility Rule for 7: There is a rule for 7, but it requires some mental math. Here's the rule: A number is divisible by 7 if the difference between twice the unit digit of the number and the remaining part of the number is a multiple of 7, or 0 An example: Is 798 divisible by 7? Double the last digit to get 16. Subtract 16 from 79. 79 - 16 = 63. Since 63 divides by 7, then 798 is divisible by 7. Another example: Is 171 divisible by 7? Double the last digit 1 to get 2. Subtract: 17 - 2 = 15. 15 doesn't divide by 7. 171 a not diisible by 7 Another example: Is 189 divisible by 7? Double the last digit to get 18. Subtract: 18 - 18 = 0. 189 is divisible by 7 Divisibility Rule for 8: A number is divisible by 8 if the last three digits are divisible by 8 For example, is 24,344 divisible by 8? The last three digits are 344, which is is divisible by 8, so 24,344 is divisible by 8. Do you see the problem with this rule? How do you know that 344 is divisible by 8? The purpose of a divisibility rule is to quickly check if a number is divisible. If you have to use long division (or a calculator) to do the rule, you might as well just do that for the original number! It's for this reason that most teachers don't show this rule. We won't include it in the list of divisibility rules we'll include at the bottom of the page. Divisibility Rule for 9: A number is divisible by 9 if its digits add to something that is divisible by 9 For example, is 65,232 divisible by 9? Since the digits add to 18, which does divide by 9, then 65,232 is divisible by 9. Another example: Is 799 divisible by 9? Since the digits add to 25, which does not divide by 9, then 799 is not divisible by 9. Divisibility Rule for 10: A number is divisible by 10 if it ends in 0 For example, 143,270 is divisible by 10 2,175 is not divisible by 10. These are the rules that are usually covered in Math 7 in Alberta. Thre are rules for 11, 12 and 13; if you're interested, check them out here. Here is a list of the Divisibility Rules in PDF format that you can print. NOTE: You've probably noticed that to use the divisibility rules, you need to have the 'times tables' memorized. Here's a practice quiz you can do online, or download, to help you learn them. |