The document outlines rules of divisibility for determining if a number is divisible by numbers 2 through 9 without performing long division. It explains that a number is divisible by 2 if the ones digit is even, by 3 if the sum of the digits is divisible by 3, by 4 if the last two digits are divisible by 4, and so on, providing examples for each rule. It notes that understanding these rules allows one to quickly determine divisibility of even very large numbers without calculations.

1. Rules of Divisibility Mrs. Young EMC 1

2. I need somebody to raise their hand and give me any two – digit number… I will then tell you what numbers this is divisible by without having do write anything down!

3. Objective To use rules of divisibility for larger numbers Definition Divisibility: the ability to determine what numbers a larger number is divisible by evenly. There are some tricks that we can use to help us determine what numbers larger numbers are divisible by without doing long division.

4. Rules of Divisibility for 2 A number is divisible by 2 if the one’s digit is even. Therefore, any number that ends with 0, 2, 4, 6, or 8 is divisible by 2 evenly. Examples: 78; 102; 1,046; 6,550

5. Rules of Divisibility for 3 A number is divisible by 3 if the sum of the digits is a multiple of three. Is 96 divisible by 3? In order to find out, we must add the digits 9 + 6 9 + 6 = 15 Is 15 a multiple of 3??? YES, which means that 96 is divisible by 3.

6. Rules of Divisibility for 3 continued… How about 108… is this number divisible by 3??? Add the digits together 1 + 0 + 8 = 9 Is 9 a multiple of 3??? YES, which means that 108 is divisible by 3!

7. Rules of Divisibility for 4 A number is divisible by 4 if the last two digits are divisible by four. Let’s take 124 for example: The last two digits in 124 are 24 Is 24 divisible by 4? YES, this means that 124 is divisible by 4!

8. Rules of Divisibility for 4 continued… How about 1,312… is this number divisible by 4??? The last two digits in 1,312 are 12 Is 12 divisible by 4??? YES, again, this means that 1,312 is divisible by 4!

9. Rules of Divisibility for 5 A number is divisible by 5 if the one’s digit is 0 or 5. So, any number that ends with a 0 or a 5 is definitely divisible by 5! Examples: 10; 95; 115; 690; 4,615

10. Rules of Divisibility for 6 A number is divisible by 6 if the sum of the digits is a multiple of three and even. Let’s look at the number 132… 132 is an even number And, if we add up all of the digits 1 + 3 + 2 = 6 6 is a multiple of 3, which means that 132 is divisible by 6.

11. Rules of Divisibility for 6 continued… Let’s try 804 804 is an even number 8 + 0 + 4 = 12 12 is a multiple of 3, which means that 804 is divisible by 6.

12. Rules of Divisibility for 7 A number is divisible by 7 : 1) Take the last digit 2) Double it 3) Then subtract it from the rest of the number. Is this number a multiple of 7?

13. Rules of Divisibility for 7 continued… Example: 203 The last digit of 203 is 3 Double 3, means 3 x 2 = 6 Subtract 6 from 20 20 – 6 = 14 Is 14 a multiple of 7?? YES, which means that 203 is divisible by 7.

14. Rules of Divisibility for 7 continued… Example: 714 Take the last digit 4, and double it. 4 x 2 = 8 Subtract 8 from 71 71 – 8 = 63 Is 63 a multiple of 7?? YES, which means that 714 is divisible by 7.

15. Rules of Divisibility for 8 A number is divisible by 8 if the last three digits are divisible by eight. Examples: 9,640 640 ÷ 8 = 80 so the whole number, 9,640, is divisible by 8 77, 184 184 ÷ 8 = 23 so 77,184 passes this divisibility test.

16. Rules of Divisibility for 8 continued… How about a huge number like: 20,233,322,496 Well, maybe you were wondering if this divisibility rule was really helpful or not. Once you get a giant number like 20,233,322,496, you start to realize what a nice trick this is to have up your sleeve! All you have to do is divide 496 by 8 to learn that the entire number is divisible by 8.

17. Rules of Divisibility for 9 A number is divisible by 9 if the sum of the digits is divisible by 9. Example: 702 Add the digits: 7 + 0 + 2 = 9 Is 9 divisible by 9? YES, which means that 702 is also divisible by 9.

18. Rules of Divisibility for 9 continued… Example: 3,276 Add the digits: 3 + 2 + 7 + 6 = 18 Is 18 a multiple of 9??? YES, which means that 3,276 is also divisible by 9.

19. Turn to your neighbor when I give you the signal, and discuss why you think this skill is useful.