Åk 6–9
 
English/فارسی
4.1 Divisibility
You have probably divided a number a good number of times. In connection with division, you have probably talked about divisibility. A whole number is divisible with another whole number if the quotient is itself a whole number.  

Example: 36 ÷ 9 = 4

If the dividend is 36 and the divisor is 9 then the quotient becomes 4.

You can determine beforehand whether a whole number is divisible with another whole number. Here are the following rules.

Here are the divisibility rules for the most common whole numbers:


A whole number is divisible by ...


...2 if the last number (ones) is even or 0. If you check the table of 2s you can see that all the numbers are even.

Example: 34 is divisible by 2, but 6,845 is not divisible by 2 because the last number is not even.


...3 if the numbers digit sum is divisible by 3.  By digit sum we mean that you add each of the digits in the number.  

Example: Is the number 252 divisible by 3?
The digit sum of 252 is 2 + 5 + 2 = 9
9 ÷ 3 = 3, which means that 252 is divisible by 3.

Is the number 361 divisible by 3?
The digit sum of 361 is 3 + 6 + 1 = 10, 10 is not devisable by  3.
361 is in other words not devisable by 3.


...5 if the last digit is a 0 or a 5. If you check the table of 5s you can see that all the numbers end in 0 or 5.

Example: 7,555 is divisible by 5, but 687 is not divisible by 5 because it doesn’t end in either a 0 or 5.


...9 if the numbers digit sum divisible by 9.

Example: Is the number 972 divisible by 9?
The digit sum of 972 is 9 + 7 + 2 = 18
18 ÷ 9 = 2, so 972 is divisible by 9.

Is the number  9,993 divisible by 9?
The digit sum of  9,993 is 9 + 9 + 9 + 3 = 30, 30 which is not divisible by 9. 9,993 is not divisible by 9.


...10 if the numbers last digit is a zero. If you check the table of 10s, you see that all the numbers end in 0.

Example: 68,760 is divisible by 10, but 9,265 is not divisible by 10 because it doesn’t end in a 0.