Divisibility Rules
Divisible by 2. If a whole number ends in 0, 2, 4, or 8, the number is called
an even number and is divisible by 2. Examples of even numbers are 238
and 1246 (
and
A number that is not even is
called an odd number. Examples of odd numbers are 113 and 2339.
Divisible by 3. If the sum of the digits of a whole number is divisible by 3,
the number itself is divisible by 3. An example is 141. The sum of the digits
is 1+4+1 = 6, which is divisible by 3. Therefore, 141 is also divisible by 3
(
Divisible by 4. If the number represented by the last two digits of a whole
number is divisible by 4, and the number itself is divisible by 4. Sample is
11,524. The last two digits represent 24, which is divisible by 4 (
Therefore, 11,524 is divisible by 4 (
).
Divisible by 5. If a whole number ends in a 0 or a 5, then the number is
divisible by five. Examples are 715 and 120 (
and
).
Divisible by 6. If a whole number is divisible by 2 and by 3, then it is
divisible by 6. An example is 738. First, 738 is even and therefore divisible
by 2. Second, 7+3+8 = 18, which is divisible by 3. Hence, 738 is divisible by
3. Since 738 is divisible by both 2 and 3, it is divisible by 6 (
).
Divisible by 8. If the number represented by the last three digits of a whole
number is divisible by 8, then the number itself is divisible by 8. An example
is 73,024. The last three digits represent the number 24, which is divisible
by 8 (
Thus, 73,024 is also divisible by 8 (
).
Divisible by 9. If the sum of the digits of a whole number is divisible by 9,
then the number itself is divisible by 9. An example is 117. The sum of the
digits is 1+1+7 = 9, which is divisible by 9. Hence, 117 is divisible by 9
(
).
Divisible by 10. The easiest divisibility test is when the digit in the ones
column is 0. When this is 0, the number is divisible by 10. An example is
3250. The last digit on the right is 0, which tells us that 3250 is divisible by
10 (
).