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Which numbers go into it?

98167572

Can the number above be divided by 3 without any remainder? Can it be divided exactly by 6 or by 9? By applying the rules below, you will be able to tell whether or not any number can be divided exactly by 2 to 10 (with the exception of 7).

Divisible

Any number can be divided by any other number (except 0) but the answer isn't always a whole number.

When a number can be divided exactly by a smaller number, without any remainder, the smaller number is a factor of it.

A number is divisible exactly by each of its factors. 10 is exactly divisible by 2. 10 is also exactly divisble by 5. 2 and 5 are factors of 10.

Divisible or not? - the rules

2
A number is divisible by 2 only if the number is even. All even numbers are divisible by 2. They end with 0, 2, 4, 6 or 8.

3
To find out if a number is divisible by 3 add together all its digits.

9+8+1+6+7+5+7+2 = 45

If the total is divisible by 3, then the original number must be divisible by 3. If you are not sure if this total can be divided by 3, add these digits together (keep on doing this until you reach a single digit - this single digit is called the digital root).

4 + 5 = 9 <--- digital root

If the digital root is 3, 6 or 9 then the original number is divisible by 3.

4
You can tell if a number is divisible by 4 if the number made by the last two digits is divisible by 4.

98167572 --> 72 / 4 = 18

You can also recognise if the last two digits are divisible by 4 by checking whether half this number, 72, is even.

5
Any number that ends in 5 or 0 is divisible by 5.

Digital Roots

A digital root is the sum of the digits in a number reduced to a single digit.

To find the digital root of

497362851063

first sum all the digits

4+9+7+3+6+2+8+5+1+0+6+3 = 54

if the total has more than one digit, sum again

5+4 = 9

9 is the digital root of 497362851063

6
A number is divisible by 6 if it is even and its digital root is divisible by 3.

98167572 is an even number and its digital root is divisible by 3.

7
There is no easy test to find out if a number is divisible by 7. Though methods have been invented they are very complicated and take as much time as doing a long division with pencil and paper.

8
A number is divisible by 8 if the number made by the last three digits can be divided by 8:

...572 / 8 = 71 r. 4 Another way: halve it, and halve it again; if it is still even then it is divisible by 8.

The example number is not divisible by 8.

9
A number is divisible by 9 if the digital root of the number is 9. If it isn't then the digital root equals the remainder that would be left after dividing by 9.