The Remainder Rule for 5 is a simple way to find the remainder when divided by 5.
Essentially, the remainder when a number is divided by 5 is the same as the remainder when the last digit of the number is divided by 5.
The last digit dictates the remainder when dividing by 5, as shown in the table below:
| Number Ending with Digits | Remainder |
|---|---|
| 0, 5 | 0 |
| 1, 6 | 1 |
| 2, 7 | 2 |
| 3, 8 | 3 |
| 4, 9 | 4 |
Note: When dividing by 5, the only possible remainders are 0, 1, 2, 3, and 4.
To find the remainder when dividing a number like 4627 by 5, we only need to look at the last digit, 7. Since 7 divided by 5 leaves a remainder of 2, 4627 divided by 5 will also have a remainder of 2.
Some more examples are:
Number: 263
- The last digit is 3.
- Dividing 3 by 5 gives a remainder of 3.
- Therefore, the remainder when 263 is divided by 5 is 3.
Number: 567
- The last digit is 7.
- Dividing 7 by 5 gives a remainder of 2.
- Therefore, the remainder when 567 is divided by 5 is 2.
Number: 482
- Take the last digit 2.
- The remainder when 2 is divided by 5 is 2.
- Therefore, the remainder when 482 is divided by 5 is 2.
Number: 7593
- Take the last digit 3.
- The remainder when 3 is divided by 5 is 3.
- Thus, the remainder when 7593 is divided by 5 is 3.
Number: 10467
- Take the last digit 7.
- The remainder when 7 is divided by 5 is 2.
- Therefore, the remainder when 10467 is divided by 5 is 2.
Proof of Remainder Rule When Dividing by 5
Let any number be N
then N can be written as 10Q + d where d represents the last digit of the number ( Ex: 8542 = 854 × 10 + 2 here Q = 854 and d = 2 )
N = 10Q + d
⇒ N mod 5 = ( 10Q ) mod 5 + d mod 5
⇒ N mod 5 = ( 5 × 2Q ) mod 5 + d mod 5
N mod 5 = 0 + d mod 5
Thus we can say that to find the remainder when dividing by 5 is equal to remainder obtained by dividing the number formed by the last digit of the number.
Thus, the remainder when 4627 is divided by 5 is the same as the remainder when 7 is divided by 5, which is 2.
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