About This Lesson
Understanding “Divisible by”
Division is the process of dividing or distributing equally. “Divisible by” and “can be evenly divided by” mean the same thing.
For example –
16 ÷ 2 = 8 exactly, so 16 is divisible by 2.
Whereas, 16 ÷ 3 = 5.33 (the result is not exact or a whole number) so, 16 is not divisible by 3.
Interesting, right? So, let’s understand the divisibility rules for each number.
Divisibility rule for 2
A number is divisible by 2, if the last digit is 0, 2, 4, 6 or 8.
So, if the number is as big as 154238, to find out whether it is divisible by 2, just see the last digit.
The last digit here is 8, which is even and divisible by 2 (2 x 4 = 8) so, 154238, is divisible by 2.
Same goes for all numbers that ends with 0, 2, 4, 6 or 8.
Divisibility rule for 3
A number is divisible by 3, if the sum of the digits is divisible by 3.
Let’s take a number – 723
Now, if we add all the digits in the number, the sum that we get will define if the number is divisible by 3. So,
7+2+3 = 12, and 12 ÷ 3 = 4 exactly, therefore, 723 is divisible by 3.
If we take the above example – 154238
1+5+4+2+3+8 = 23, and 23 ÷ 3 = 7.66 (not a whole number)
Therefore, 154238 is not divisible by 3.
Divisibility rule for 4
A number is divisible by 4, if the number formed by the last two digits is divisible by 4.
For example, let’s take the number 516
The last two digits formed is 16, and 16 ÷ 4 = 4,
Therefore, 516 is divisible by 4.
Another example is 922.
The last 2 digits – 22 ÷ 4 = 5.5 (not a whole number)
Therefore, 922 is not divisible by 4.
Divisibility rule for 5
A number is divisible by 5, if the last digit is either 0 or 5.
For example, 289435, the number is large. But, the last digit is 5. Therefore, 289435 is divisible by 5.
289435 ÷ 5 = 57887 (exact and whole number)
A short number, like 280 is also divisible by 5 as the last digit is 0.
280 ÷ 5 = 56.
Divisibility rule for 6
A number is divisible by 6, if it is divisible by 2 AND 3.
Since, 2 x 3 = 6, the number must be divisible by 2 and 3 to be divisible by 6.
For example, let’s take 168,
8 being the last digit of 168, is divisible by 2 (according to the divisibility rule of 2).
Also, 1+6+8 = 15, and 15 ÷ 3 = 5, (according to the divisibility rule of 3, 168 is divisible by 3).
Therefore, 168 is divisible by both 2 and 3.
Hence, 168 is also divisible by 6.
168 ÷ 6 = 28 (whole and exact number)
Divisibility rule of 7
If the last digit of a number is doubled and then subtracted from the rest of the number, and the answer is 0 or is divisible by 7, then the number is divisible by 7.
So, let’s take the number 392
The last digit is 2, when doubled, it’s 4 (2+2=4)
The rest of the number – 39. So, 39 – 4 = 35.
And, we know that 7 x 5 = 35.
Therefore, 392 is divisible by 7.
Another one?
686
The last digit when doubled is 12 (6+6=12)
And, 68 – 12 = 56.
So, 7 x 8 = 56. Therefore, 686 is divisible by 7.
Divisibility rule of 8
A number is divisible by 8, if the number formed by the last three digits is divisible by 8.
For example, take 109816
Now, the last 3 digits of the number is 816.
816 ÷ 8 = 102, therefore, 109816 is divisible by 8.
109816 ÷ 8 = 13727.
Let’s take 5684,
Last 3 digits are 684.
684 ÷ 8 = 85.5 (Not exact and a whole number)
Hence, 5684 is not divisible by 8.
Divisibility rule of 9
A number is divisible by 9, if the sum of the digits is divisible by 9.
Let’s take 549.
The sum of all the digits in the number is
5+4+9 = 18,
18 is divisible by 9 (9 x 2 = 18). Therefore, 549 is divisible by 9.
Now, let’s take the above example, 109816.
1+0+9+8+1+6 = 25.
25 is not divisible by 9, hence, 109816 is not divisible by 9.
Divisibility rule of 10
A number is divisible by 10, if the last digit is 0.
This one’s easy. Just see the last digit, and if it is 0, the number is divisible by 10.
So, you tell us, if 234897610 is divisible by 10?
Now that you have understood the divisibility rules for all the numbers from 2 to 10, let’s take a random number and see how many numbers from 2 to 10 it is divisible by.
Number- 35,120
35,120 is divisible by 2 since the last digit is 0.
35,120 is not divisible by 3. The sum of the digits (3+5+1+2+0 = 11) is 11, and 11 is not divisible by 3
35,120 is divisible by 4 since last two digits – 20 is divisible by 4 (4 x 5 = 20)
35,120 is divisible by 5 since the last digit is 0.
35,120 is not divisible by 6 since it is not divisible by both 2 and 3.
35,120 is not divisible by 7 since 3512 is not divisible by 7.
35,120 is divisible by 8 since the last 3 digits are 120, and 120 is divisible by 8.
35,120 is not divisible by 9 since the sum of the digits is 11, and 11 is not divisible by 9.
35,120 is divisible by 10 since the last digit is 0.
Hence, 35,120 is divisible by 2, 4, 5, 8 and 10.
Fun, wasn’t it? With the help of these divisibility rules, your child whether in grade 3, grade 4 or 5th grade, can easily solve sums in division, word problems and multiples in a jiffy.
Want more ideas for Divisibility Rules?
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