Divisibility
Divisible - When one number can be divided
by another and the result is an exact whole
number (an answer with no remainders).
3
1
3
3
9
3
1
2
3
7
r1
Divisibility Rules
Dividing by 1:
All numbers are divisible by 1.
Try dividing any number you can think of by 1.
Divisibility Rules
Dividing by 2:
4070
If a number is even it will always divide by 2.
There is a quick way to test if a number can be divided by 2.
Simply look at the last digit. If it is even (0,2,4,6 or 8)
then the number is divisible by 2.
Divisibility Rules
Dividing by 3:
If the sum of all the digits in
a number is a multiple of 3
then it is divisible by 3.
153
1+5+3=9
9 can be divided equally by
3 so 153 is divisible by 3.
Divisibility Rules
Dividing by 4:
1 543 612
Look at the last two digits of
any number. If they can be
divided equally by 4 then the
whole number is divisible by
4, no matter how large the
number!
12 is divisible by 4.
This means that 1 543 612 is also divisible by 4.
If a number ends in 00 it is also divisible by 4.
Divisibility Rules
Dividing by 5:
A simple rule for dividing by
5. If a number ends in a 0 or
a 5 then it is divisible by 5!
6240
Divisibility Rules
Dividing by 6:
This rule is a little harder as
you have two steps to follow.
To test if a number is divisible by 6, you must
first see if you can divide it by 2 and then by 3.
6924
6+9+2+4=21
We know it can be divided by 2
as it ends with an even number.
We know it can be divided by
3 because 21 is divisible by 3.
6924 can be divided by both 2
and 3 so it is also divisible by 6.
Divisibility Rules
Dividing by 7:
To test if a number is divisible by 7, take the last number and double
it, then subtract it from the number made by the other digits. The
answer must be divisible by 7.
Let’s try one together with 826.
826
826
Double the last number.
6+6=12
Now take the number made by the other digits
and subtract 12 from this.
82–12=70
We can divide 70 by 7,
therefore 826 is divisible by 7.
Divisibility Rules
Dividing by 8:
There are no simple tests for numbers divisible by 8. However, if you
have a large number you can make it simpler by only looking at the
last three digits.
4567248
8
2
3
1
4
8
You do not have to try dividing the
whole number, just the last 3 digits.
248 is divisible by 8, therefore
4567248 is divisible by 8 too.
Divisibility Rules
Dividing by 9:
Our last few rules for divisibility have
been quite tricky! But don’t worry the
rule for 9 is straight forward.
Simply add all the digits to see if the total is divisible by 9.
225
2+2+5=9
562
5+6+2=13
Divisibility Rules
Dividing by 10:
To test if a number is divisible by 10 simply look at the last digit.
If it is a zero it will always be divisible
by 10, no matter how large the number!
153469780
652430
456