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Divisibility
Rules!
What is Divisibility?
Divisibility means
that after
dividing, there will
be no remainders.
The divisor can
evenly divide into
the dividend.
356,821
• Can you tell by just
looking at this
number if it is
divisible by 2?
• by 3?
• by 4?
• by 5?
• by 6 ?
• by 9?
• By 10?
• The divisibility
rules can help
you!
Divisibility rules help you learn
shortcuts to tell when a number
can be divided by another
number without any remainders.
Divisibility by 2
• A number is
divisible by 2
if the number
is even.
18 ÷ 2 = 9
22 ÷ 2 = 11
(18 and 22: Notice that
both of these
dividends are even.)
21 ÷ 2 = 10 R1
(21: not an even
number.)
Now You Try
Are these numbers divisible by 2?
a)79,458
b)1,279
c)6,249
d)51,553
e)19,050
f)35,792
Divisibility 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: 1 + 3 + 5 = 9
Yes, 135 is divisible by 3 because the sum of the
digits is divisible by 3.
Dividing by 3
For example, take the number
738
Add up the digits of the number
7 + 3 + 8 = 18
Is 18 divisible by 3?
If that number is divisible by 3, then
the original number is
If your sum is still a big number,
continue to add the digits
1+8=9
Is 9 divisible by 3?
Now You Try
Are these numbers divisible by 3?
a)639
b)56
c)86
d)360
e)468
f)2,511
Dividing by 4
• If the last 2 digits together are divisible by 4
Example: 72,624
Is 24 divisible by 4?
Now You Try
Are these numbers divisible by 4?
a)97,584
b)123,261
c)48,156
d)53,920
e)25,767
f)13,224
Divisibility by 5
• A number is divisible by
5 if it ends in 0 or 5.
25 ÷ 5 = 5
23 ÷ 5 = 4 R3
Now You Try
Are these numbers divisible by 5?
a)198,554
b)6,890
c)31,345
d)68,902
e)371,845
f)20,001
Divisibility by 6
• A number is
divisible by 6
if it is divisible
by both 2 AND
Is 42 divisible by
6?
Think:
Is 42 divisible by 2?
Is 42 divisible by 3?
3.
• Is 51 divisible
by 6?
Hint: Is it an even
number?
Now You Try
Are these numbers divisible by 6?
a)897
b)258
c)630
d)345
e)84
f)8,235
Divisibility by
• A number is •
divisible by 9
if the sum of •
its digits is •
divisible by
9.
369 is divisible by
9
because
3 + 6 + 9 =18
1 + 8 = 9
and
9 is divisible by
9.
Dividing by 9
• For example, take the number
924,561
Add up the digits of the number
9 + 2 + 4 + 5 + 6 + 1 = 27
Is 27 divisible by 9?
If that number is divisible by 3, then
the original number is
If your sum is still a big number,
continue to add the digits
2+7=9
Is 9 divisible by 9?
Now You Try
Are these numbers divisible by 9?
a)55,578
b)22,398
c)91,548
d)17,903
e)32,490
f)83,402
Divisibility by
• A number is
divisible by
10 if it
ends in 0.
• 30 ÷ 10 = 3
• 340 ÷ 10 = 34
• 67 ÷ 10 = 6 R7
• 784 ÷ 10 =78 R4
Now You Try
Are these numbers divisible by
10?
a)24,578
b)39,800
c)48,003
d)19,030
e)490,870
f)65,432
Is it divisible by:
2
444,555,448
26,350
74,673,042
61,616,168
732,510
9,623,205
3
4
5
6
9 10
Is it divisible by:
2
123,456,789
58,468,240
52,301,042
246,813,579
135,790,135
813,423,700
3
4
5
6
9 10
After all, divisibility
rules!
THE END