Divisibility Rules

There are some special rules that make multiplying, factoring and dividing a lot easier.

The first rule is that any number that is divisible by 2 has to be even and if the number is even the number is divisible by 2.

8 is even so it is divisible by 2
8÷2=4
22 is even so it is divisible by 2
22÷2=11
23 is odd therefore it is not divisible by 2.
23÷2=11.5 

Any number that is divisible by 10 will end in a zero.  If a number ends in a zero, it is divisible by 10.

130 ends in a 0 so it is divisible by 10
130÷10=13
122 does not end in a zero so it is not divisible by 10
122÷10=1.22

Any number that is divisible by 5 will end in 5 or a 0.  If a number ends in 5 or 0, it is divisible by 5.

125 ends in a 5 so it is divisible by 5
125 ends in 5 so it is divisible by 5
125÷5=25
160 ends in 0 so it is divisible by 5
160÷5=32
201 does not end in 5 or 0 so it is not divisible by 5.
201÷5=40.2

If a number that is divisible by 3, then the sum of its digits is divisible by 3.  If the digits of a number add up to something other than 3, then it is not divisible by 3.

114 is a number whose sum of digits equals 6 which is divisible by 3 so 114 is divisible by 3.
114÷3=38
514 is a number whose sum of digits equals 10 which is not divisible by 3 so 114 is not divisible by 3.
514÷3=171.333333....

If a number that is divisible by 4, then the last 2 digits are divisible by 4.  If the last 2 digits of a number are not divisible by 4, then the number is not divisible by 4.

724 is a number such that the last 2 digits that are divisible by 4 so 724 is divisible by 4.
724÷4=181
718 is a number such that the last 2 digits that are not divisible by 4 so 724 is not divisible by 4.
718÷4=179.5

Exercises:

Find out if the following numbers are divisible by 2, 3, 5, or 10 or not divisible by any of the numbers.

25, 2864, 1290, 441, 1236, 445, 221, 708, and 433.