Divisibility Dreams
www.MaxLearning.Net 
Any number is
divisible by any other number
(except zero). But when you need
to know if a number is exactly
divisible (with no remainder)
by another, the following rules
can tell you without
having to actually perform the
division. This makes it a dream
when your task is to factor a
larger number into its smaller
multipliers. 
Topic 
Text 
Video 
Divisibility Dreams Reference Sheets
(3
across)
Cut out and keep one of these
with you until you memorize
each rule. 
1 page 

A number is exactly
divisible by: 


2 
If it
is even (ends in 0, 2, 4, 6, 8)
[976]. 


3 
If its
SOD (Sum Of
Digits) is divisible by 3
[546: 5+4+6 = 15]. 


4 
If it
is even
and its last 2 digits = 00
[300] or are divisible by 4 [316]. 


5 
If it ends in 0
[230] or 5 [765]. 


6 
If it follows
rules for both 2 and 3 [462:
4+6+2 = 12]. 


7 
If its
1st digit/s
minus twice its
last digit
= 0 [147:
14
– (2×7)
= 14 – 14 = 0] or
is divisible by 7 [91:
9
– (2×1)
= 9 – 2 = 7].
*
To seek 7 is
futile
(first minus twice
last). 


8 
If it is even
and its last 3 digits =
000 [5000] or
are divisible by 8 [3888]
or twice the
first two
of the 3 digits plus the
last
is divisible by 8 [3152:
(2×15)
+
2
= 30 + 2 = 32].
* He ate(8)
& was too full
(twice first
plus last). 


9 
If its
SOD (Sum Of
Digits)
is divisible by
9 [2754: 2+7+5+4 =
18]. 


10 
If it ends in 0
[6370]. 


11 
If SOD(odd)
– SOD(even)
= 0 [572:
(5+2)
–
7
= 7 – 7 = 0]
or is divisible by 11
[2816:
(2+1)
– (8+6)
= 3 – 14 = 11]. 


12 
If it follows
rules for both 4 and 3
[924: 9+2+4 =
15]. 


