What is Divisibility? Divisibility means that after dividing, there will be No remainder.

356,821 Can you tell by just looking at this number if it is divisible by 2? by 5? by 10? by 3 ? by 9? By 6? The divisibility rules can help YOU!

help you learn to tell when a number can be divided by another number with. Divisibility Rules help you learn shortcuts to tell when a number can be divided by another number with NO REMAINDER.

Dividing By 1 All numbers are divisible by 1

Now You Try Are these numbers divisible by 1? a) 578 b) 1201 c) 465

Dividing by 2 All even numbers are divisible by 2 Even numbers are numbers that end with either 2, 4, 6, 8, or 0 18 ÷ 2 = 9 22 ÷ 2 = 11 Notice that both of these numbers are even. 21 ÷ 2 = 10 R1 NOT EVEN

Now You Try Are these numbers divisible by 2? a) 458 b) 1279 c) 759 Not an even number Not an even number

Dividing by 3 A number is divisible by 3 if the sum of the digits is divisible by 3. Is the number 135 divisible by 3? Add the digits : = 9 Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

Now You Try Are these numbers divisible by 3? a) 639 Sum of =18 b) 56 Sum of 5+6 =11 NO c) 738 Sum of =18

Dividing by 4 If the last 2 digits together are divisible by 4 or take your number, divide it by 2. Then divide that answer by 2, and if you get an EVEN NUMBER then it is divisible by 4 2)2) EVEN 2)2) EVEN Example 360 4)4) Example 384

Now You Try Are these numbers divisible by 4? a) 584 b) 261 4)4) )4) r1 NO Take the last 2 digits and divide by 4

Dividing by 5 If the number ends in 5 or 0 25 ÷ 5 = 5 23 ÷ 5 = 4 R3 NO

Now You Try Are these numbers divisible by 5? a) 554 b) 6890 c) 345

Dividing by 6 If the number is divisible by 2, AND... If the number is divisible by 3

Now You Try Are these numbers divisible by 6? a) 897 b) 258 c) 630 No it is not EVEN EVEN, Sum of =15 EVEN, Sum of =9

Dividing by 7 There is no special rule to help you know if a number is divisible by 7…

Now You Try Are these numbers divisible by 7? a) 500 b) 49 c) 2100

Dividing by 8 If the last three digits are divisible by 8 If the number is divisible by 2, then by 2 again, and then by 2 again So what type of number does it have to be? A number that has been cubed.

Now You Try Are these numbers divisible by 8? a) 568 2)2) Even 2)2) Even 2)2) b) 396 2)2) 198 Even 2)2) Odd NO Take the last 3 digits and divide by 2, then divide by 2, then divide by 2

Dividing by 9 Similar to dividing by 3 Add up digits If that number is divisible by 9 then your number is divisible by 9

Dividing by 9 If that number is divisible by 9, then the original number is If your sum is still a big number, continue to add the digits Add up the digits of the number 27 Is 27 divisible by 9? = 9 For example, take the number 924, =

Now You Try Are these numbers divisible by 9? a) 578 b) 399 c) 144 Sum of =20 NO Sum of =21 NO Sum of =9

Dividing by 10 If the number ends with a 0 30 ÷ 10 = ÷ 10 = ÷ 10 = 6 R7 784 ÷ 10 =78 R4

Now You Try Are these numbers divisible by 10? a) 5782 b) 390 c) 45

Dividing by 11 There is no special rule to help you know if a number is divisible by 11…

Now You Try Are these numbers divisible by 11? a) 99 b) 88 c) 121

REVIEW Divisible by 1 Divisible by 2 Divisible by 3 Divisible by 4 Divisible by 5 Divisible by 6 Divisible by 7 Divisible by 8 Divisible by 9 Divisible by 10 Divisible by 11 Thumbs up if you remember the rule.

After All… DIVISIBILITY Rules Take Out Your Study Guide!!!

RULES FOR DIVISIBILITY #1 A Number Is Divisible By: IF The last digit is even (0, 2, 4, 6, 8) The last 2 digits are divisible by 4 The sum of the digits is divisible by 3 The last digit is 0 or 5 It is divisible by 2 and 3 The last 3 digits are divisible by 8 The sum of the digits is divisible by 9 The last digit is 0

IS THE NUMBER DIVISIBLE EXACTLY BY? WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8. Number ) 360 y 3+6 = 9 y y yy 2)2) 180 2)2) y yy 2)2) )2) )2) #2