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. |