When dividing by 4, the remainder helps determine whether a number is fully divisible by 4 or if a smaller remainder is left over. To find the remainder when a number is divided by 4, you can look at the last two digits of the number:
- If the last two digits form a number that is divisible by 4, the remainder is 0.
- If the last two digits form a number that gives a remainder of 1 when divided by 4, the remainder is 1.
- If the last two digits form a number that gives a remainder of 2 when divided by 4, the remainder is 2.
- If the last two digits form a number that gives a remainder of 3 when divided by 4, the remainder is 3.
For example, with the number 1958, we focus on the last two digits, which are 58.
Since any digits before the last two contribute a multiple of 100 (and 100 is divisible by 4), they don't affect the remainder when dividing by 4.
So, we take 58 and divide it by 4. The calculation shows that 58 ÷ 4 = 14 with a remainder of 2.
Therefore, when we divide 1958 by 4, the remainder is 2.
Some other examples are:
- Number: 102
- Last two digits: 02 → Remainder when divided by 4 is 2
- Number: 145
- Last two digits: 45 → Remainder when divided by 4 is 1
- Number: 256
- Last two digits: 56 → Remainder when divided by 4 is 0
- Number: 379
- Last two digits: 79 → Remainder when divided by 4 is 3
Note: When dividing by 4, the only possible remainders are: 0, 1, 2, and 3.
Proof of Remainder Rule When Dividing by 4
Let any number be N, then N can be written as 100Q + d where d represents the last two digits of the number ( Ex: 8542 = 85 × 100 + 42 here Q = 85 and d = 42 )
N = 100Q + d
⇒ N mod 4= ( 100Q ) mod 4 + d mod 4
⇒ N mod 4 = ( 4 × 25Q ) mod 4 + d mod 4
N mod 4 = 0 + d mod 4
Thus we can say that to find the remainder when dividing by 4 is equal to remainder obtained by dividing the number formed by the last 2 digits of the number.
Thus, the remainder when 1958 is divided by 4 is the same as when 58 is divided by 4, which is 2.
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