### Divisibility by 3, 6, 9

```Divisibility by
3, 6, 9
Review of Divisibility
A number can be divided by…
÷2
when…
… ending digit is EVEN (2, 4, 6, 8, 0)
÷5
when…
… ending digit is 5 OR 0
÷ 10
when…
… ending digit is 0
Divisibility by 3, 6, 9
Example:
We can ÷ “3”
471 ÷ 3?
…when the sum of all
digits is a number that
can be divided by 3
4 + 7 + 1 = 12
12 ÷ 3?
yes, so…
471 ÷ 3 = yes
Divisibility by 3, 6, 9
Can we ÷ 3??
78 ÷ 3
7 + 8 = 15
 15 ÷ 3 = yes
458 ÷ 3
4 + 5 + 8 = 17
 17 ÷ 3 = no
9270 ÷ 3
9 + 2 + 7 + 0 = 18
 18 ÷ 3 = yes
Divisibility by 3, 6, 9
Example:
We can ÷ “6”
108 ÷ 6?
…when the number can
be divided by 2 AND 3
 last digit ÷ 2
 sum of digits ÷ 3
Last digit = 8
8 ÷ 2? Yes
1+0+8=9
9 ÷ 3 = yes
therefore… ÷ 6
Divisibility by 3, 6, 9
Can we ÷ 6??
7602 ÷ 6
last digit = 2
 2 ÷ 2 = yes
7 + 6 + 0 + 2 = 15
 15 ÷ 3 = yes
3783 ÷ 6
last digit = 3
 3 ÷ 2 = no
3 + 7 + 8 + 3 = 21
 21 ÷ 3 = yes
Divisibility by 3, 6, 9
Example:
We can ÷ “9”
513 ÷ 9?
…when the sum of all
digits is a number that
can be divided by 9
5+1+3=9
9 ÷ 9?
yes, so…
513 ÷ 9 = yes
Divisibility by 3, 6, 9
Can we ÷ 9??
7470 ÷ 9
7 + 4 + 7 + 0 = 18
18 ÷ 9 = yes
*can also be ÷ 3
2568 ÷ 9
2 + 5 + 6 + 8 = 21
 21 ÷ 9 = no
*BUT can be ÷ 3
Divisibility by 3, 6, 9
Can it be ÷ 3, 6, or 9??
a) 7602?
b) 6246?
c) 578,564?
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