可分性规则。所以首先，让我们开始谈论几个简单的问题。 Is 56 divisible by 7? Is 50, divisible by 13? Theoretically, those are questions you should be able to answer with little problem.

第一次答案当然，是是的，56等于7次8.当然的第二个答案是否，13确实进入52但是 it does not go into 50. So first of all I'll just mention, if these are not questions that you can answer just by looking at them, probably you need to practice your times tables a little bit more.

你真的需要把你的基本时期表达下来，这样就像这样的问题实际上很容易。 现在，一个稍微更难的问题是长号被3所以3.好吧，没有人希望你在头脑中做这个分裂。 We can't do the full division of find the quotient, but we can use it the divisibility rule to answer the question, and the test loves divisibility roles.

So first of all, divisibility by 2. Of course, all even numbers that are divisible by 2. To tell whether a large numbers even, all we have to do is look at the last digit. If the one's digit is even, then the number is even. 所以我们有这些大数字，我们可以忽略其余的数字，看看一个人的位置。

在一个人的位置，我们看到5,1，7,3，那些都是奇数的，但6是偶数。这意味着中间是一个数字是6， that's the only even number, the only number divisible by 2. So that's divisibility by 2. 可分配到5.这是另一个涉及查看最后一位数字的可分配规则。

If the last digit is a 5 or 0, then the number is divisible by 5, otherwise, it isn't. So again we have big numbers like these, we can ignore the rest of the number and just look at that last digit. 在契约中，我们有一个5的最后一位，所以数字是可被5所以5，但其他数字不在5或0中结束，因此它们不可分割为5。

So both of those rules, divisibility by 5 and divisibility by 2, those just involve looking at the one's place and nothing else. 现在，规则为4.此规则类似，这里，我们看最后两位数， the ten's place and the one's place, so we have to look at two digits. If the last two digits for me to digit number divisible by 4, then the entire number is divisible by 4.

So again, our same list of long numbers, look at those last two digits and think of them as two digit numbers, 55, 41, 96, 37, 33. The only one amongst those that is divisible by 4 is 96, 96 is a number divisible by 4. So that means that hole, middle number is divisible by four. Now, divisibility for 3, the test loves this rule.

This rule is a little different. Here, we add up all the digits of the number. If the sum of the digits is divisible by 3, then the number is divisible by 3 and if the sum of the digits is not divisible by 3, the number is not divisible by 3. So for example with 135 we add 1 plus 3 plus 5, that's 9, so 9 is divisible by 3, 135 must be divisible by 3.

有734，我们加入7加3加4，即等于14.由于14不可分割，因此 我们知道734不可分割的3. 1296，我们加入1加2加9加6，即18。 由于18以3即3，因此1296必须可分解3.所以它与大数字相同的方式。

Here's the question we had at the very beginning of the module. So is that large number divisible by 3? 嗯，这是我注意到的，我注意到中间3加3加4等于10。 I can take the 5 plus 5 that equals 10. And that only leaves a 1, a 0, a 2 and another 1, and those add up to 4.

So that means that everything adds up to 24. The sum of the judges is 24, which is divisible by 3, so the original number must be divisible by 3. So all we have to do is add up of the digits, and then see if that's divisible by 3 and then that tells us whether the number overall is divisible by 3. The Divisibility Rule for 9.

This is exactly like the rule for 3. Add all the digits, if the sum of the digits is divisible by 9, then the number is divisible by 9. If the sum of the digits is not divisible by 9, the number is not divisible by 9. So for example 1296 we found in the last few slides that the sum of this was 18. The sum is divisible by 9, so 1296 must be divisible as well.

3072，我们将这些数字添加到12中，我们得到12的总和。因此，数字的总和已被3分开，但不是9， so the number is divisible by 3 but not 9. Notice incidentally, 3072, the last two digits number, 72 is divisible by 4. So that's a number that would be divisible by 3 and by 4, which would mean it's divisible by 12.

We can also use the divisibility rule for 9, for larger numbers. So is this large number divisible by 9? Well, we already found out sum of the digits is 24. So 24 is divisible by 3 but not by 9. 原来的号码,9位number is divisible by 3, but not by 9. The Divisibility Rule for 6.

Here, we're gonna have a combination. In order to be divisible by 6, a number must be, a, divisible by 2, and b, divisible by 3. We checked divisibility by 2 by looking at the last digit, making sure that it's even. And we checked the visibility by 3 by finding the sum of the digits.

So any even number divisible by 3 has to be divisible by 6. Is 1296 divisible by 6? 好吧，首先，我们知道甚至是什么，我们发现的数字的总和是18，它是可被3的。 Therefore 1296 is divisible by 6. Is this long number divisible by 6?

Well, clearly it's even, that's easy to determine. We add the digits at the first three that up to 15. The second three digits at up to 14. The last three digits at up to 17. 15 plus 17 plus 14 is 46. The sum of the digits is not divisible by 3, so the original number is not divisible by 3 or by 6.

In this video we discuss the most common divisibility rules, the rules for 2, 5, 4, 3, 9 and 6.