Remainder Calculation Using Divisibility Rule for 3

To find the remainder when a number is divided by 3 without performing the actual long division, we can use the divisibility rule of 3. This rule states that the remainder of a number when divided by 3 is the same as the remainder of the sum of its digits when divided by 3.

Applying the Divisibility Rule

The number given is 379843.

First, we need to find the sum of the digits of this number:

Sum = 3 + 7 + 9 + 8 + 4 + 3

Let's calculate the sum:

Sum = 10 + 9 + 8 + 4 + 3

Sum = 19 + 8 + 4 + 3

Sum = 27 + 4 + 3

Sum = 31 + 3

Sum = 34

Finding the Remainder of the Sum

Now, we need to find the remainder when this sum (34) is divided by 3.

We perform the division: $$ 34 \div 3 $$

We know that $3 \times 11 = 33$.

So, the remainder is:

Remainder = $34 - 33$

Remainder = 1

Conclusion

According to the divisibility rule of 3, the remainder when 379843 is divided by 3 is the same as the remainder when the sum of its digits (34) is divided by 3, which is 1.