Divisibly rules
"Divisible By" means "when you divide one number by another the result is a whole number"
or can be can be evenly divided by
Rule for 2: The number is divisible by 2 if the number ends with the last digit is even being
0,2,4,6,8.
Example: 36 is divisible by 2? Yes because,
1. Is a even number
2.Ends with a 6 which is even
3. 36 goes into 2 = 18 times also an even number
36 is a multiple of 2: 2*18=36
Example 2: Is 17 divisible by 2?
No, why not because it doesn't end with an even number like 0,2,4,6,8 and is not an even number
it's an odd number.
17/2= 8.5 not being ending evenly
17 is not a multiple of 2: 2*?=17
Rule for 3: The sum of the digits is divisible by 3
Example 1: 1221 is it divisible by 3? why?
Yes, because when you add all of the integers 1+2+2+1 and you get 6.
Thereafter, you get 6 and you check whether 6 is divisible by 3 (6/3=2) and it is. Which then
makes 1221 divisible by 3.
1221 is a multiple of 3: 3* 407=1221
Example 2: 116, Is it divisible by 3?
1+1+6=8 is 8 divisible by 3? No, because 8/3= 2.67 which is not a number divisible by 3.
116 is not a multiple of 3: 3*?=116
Rule for 4: The last 2 digits are divisible by 4
Example 1: 216
Are the last two numbers divisible by 4? 16
16/4=4 therefore it is divisible by 4.
Example 2: 415 is this number divisible by 4? Let's check the last two numbers 15
Is 15 divisible by 4? (15/4=3.75) No it is not divisible by 4.
Rule for 5: The last digit is 0 or 5
Example 1: 105
The rule is if it ends with 5 or 0 then it is divisible by 5.
Now let's check does it end with a 0 or 5? It ends with 5 therefore it is divisible by 5.
105 is also a multiple of 5: 5&21=105
Example 2: 367
Does it end with a 0 or a 5? No then 367 is not divisible by 5
367 is not a multiple of 5: 5*?=367
Rule for 6: The number is divisible by both 2 and 3. Therefore it follows the rules of 2 as
well as 3.
Example 1: 24
Does it end with 2,4,6,8? YES which makes it even therefore it now follows both rule for 2 and
6.
When adding all of the integers 2+4 =6 Is 6 divisible by 6? Yes it equals to one which
makes it follow now rules 3 and 6.
The rule of 2 and 3 now applies for the rule of 6 because if it ends with even number then
it is divisible by 2 and 6. If when adding all integers and then dividing by 6 and you get a whole
number then it follows the rules for 3 and 6.
24 is a multiple of 6: 6*4=24
Example 2: 208
Is it even? YES
When you add all integers what do you get 2+8=10 is 10/6 a whole number? No then it is not
divisible by 6.
208 is not a multiple of 6: 6*?=208
Rule for 9: The :sum of the digits is divisible by 9 (similar to rule of 3)
Example 1: 1233
Add all integers 1+2+3+3=9
Is 9 divisible by 9? YES 9/9=1 Therefore it makes 1233 divisible by 9.
1233 is a multiple of 9: 9*137= 1233
Example 2: 2015
Add all integers 2+0+1+5=8. Is 8 divisible by 9?
No, because 8/9=0.89 which is not whole number.
2015 Is not a multiple of 9: 9*?=2015
Rule for 10: The number ends in 0 than it is divisible by 10.
Example 1: 20
Does it end with a 0? Yes therefore it is divisible by 10.
20 is a multiple of 10: 10*2=20
Example2: 21
Does it end with a zero? No it ends with a 1 therefore it is not divisible by 10.
21 is not a multiple of 10: 10*?=21
