Divisibility Rules
What Are Divisibility Rules?
• They are a quick way to tell if one number can
be completely divided into another without a
remainder
• For example, 32 is divisible by 2 since 32 ÷ 2 =
16.
• We will learn the rules for dividing by 2, 3, 5
and 10.
Divisibility Rules
Divisibility by 2
• A number is divisible by 2 if
the last digit is even (0, 2, 4,
6, or 8)
Divisibility by 3
• A number is divisible by 3 if
the sum of all the digits is
divisible by 3.
• 13 156 is divisible by 2 since
it ends with an even
number (6)
• 16 848 is divisible by 3 since
1 + 6 + 8 + 8 + 4 = 27 and 27
÷3=9
Divisibility Rules
Divisibility by 5
• A number is divisible by 5 if
the last digit is 0 or 5
Divisibility by 10
• A number is divisible by 10
is the last digit is 0.
• The number 13 590 is
divisible by 5 since it ends
with 0.
• 13 595 is also divisible by 5
since it ends with 5
• 17 480 is divisible by 10
since it ends with 0
Divisibility Rules
Divisibility by 4
• A number is divisible by 4 if
the last two digits are both
0 or if they are divisible by 4
(or by 2 twice)
• 26 524 is divisible by 4 since
24 ÷ 4 = 6 or 24 ÷ 2 = 12 and
12 ÷ 2 = 6
Divisibility by 6
• A number is divisible by 6 if
it can be divided by 2 and
by 3 (it must be an even
number and the sum of all
its digits must be divisible
by 3)
• 153 174 is divisible by 6
since it is an even number
and 1 + 5 + 3 + 1 + 7 + 4 = 21
and 21 ÷ 3 = 7.
Divisibility Rules
Divisibility by 8
• A number is divisible by 8 if
its last three digits are all 0
or if the number formed by
the sum of these last three
digits is divisible by 8
• 147 608 is divisible by 8
since 608 ÷ 8 = 76
Divisibility by 9
• A number is divisible by 9 if
the sum of its digits is
divisible by 9
• 236 232 is divisible by 9
since 2 + 3 + 6 + 2 + 3 + 2 =
18 and 18 ÷ 9 = 2