Divisibility Test of Numbers
Dividing By 2: A number is divisible by 2 if the last digit
is even.
Dividing By 3: A number is divisible by 3 if the sum of all
the digits is divisible by 3.
Ex [1] 34,164 is divisible by 3 because 3+4+1+6+4 = 18
which is divisible by 3.
To find the remainder of a number divided by 3, add the
digits and find that remainder. So if the
digits added together equal 13 then the number has a
remainder of 1 since 13 divided by 3 has a
remainder of 1.
Dividing By 4: A number is divisible by 4 if the last 2-digits
are divisible by 4.
Ex [1] 34,164 is divisible by 4 because 64 is divisible
by 4.
To find the remainder of a number divided by 4 take the
remainder of the last 2 digits. So if the
last 2-digits are 13 then the number has a remainder of 1
since 13 divided by 4 has a remainder
of 1.
Dividing By 5: A number is divisible by 5 if the last digit
is a 5 or a 0.
To find the remainder of a number divided by 5 simply use the
last digit. If it is greater than 5,
subtract 5 for the remainder.
Dividing By 6: A number is divisible by 6 if it is
divisible by 2 and by 3.
Ex [1] 34,164 is divisible by 6 because it is divisible
by 2 and 3.
Dividing By 7: A number is divisible by 7 if the following
is true:
1. Multiply the
ones digit by 2.
2. Subtract
this value from the rest of the number.
3. Continue
this pattern until you find a number you know is or is not divisible by 7.
Ex [1] 7203 is divisible by 7 because
a) 2x3= 6.
b) 720 – 6 = 714 which is divisible by 7.
Ex [2] 14443 is not divisible by 7 because
a) 3x2= 6.
b) 1444 – 6 = 1438.
c) 8x2= 16.
d) 143 – 16 =
127 which is not divisible by 7.
Dividing By 8: A number is divisible by 8 if the last
3-digits are divisible by 8.
Ex [1] 34,168 is divisible by 8 because 168 is divisible
by 8.
Dividing By 9: A number is divisible by 9 if the sum of the
digits is divisible by 9.
Ex [1] 34,164 is divisible by 9 because 3+4+1+6+4 = 18
which is divisible by 9.
Dividing By 10: A number is divisible by 10 if the last digit
is a 0.
Dividing By 11: A number is divisible by 11 if this is true:
Step1: Add all even place digits of a number
Step2: Add odd place digits of a number
Step3: Subtract 1st Step from the 2nd Step
If this value
is 0 then the number is divisible by 11. If it is not 0 then this is the
remainder after dividing by 11 if it is positive. If the
number is negative add 11 to it to get the remainder.
Ex [1] 6613585 is divisible by 11 since (5+5+1+6) –
(8+3+6) = 0.
Dividing By 12: A number is divisible by 12 if it is divisible
by 3 and by 4.
Ex [1] 34,164
is divisible by 12 because it is divisible by 3 and 4.