Without actual division find the remainder when 379843 is divided by 3.

Options

A. 0
B. 2
C. 1
D. 4

Answer

To find the remainder when 379843 is divided by 3 without performing actual division, we can use the divisibility rule for 3. The rule states that a number is divisible by 3 if the sum of its digits is divisible by 3. Therefore, we will first find the sum of the digits of the number 379843.

**Step 1: Sum the digits of 379843.**
- The digits are: 3, 7, 9, 8, 4, and 3.
- Calculate the sum:
\( 3 + 7 + 9 + 8 + 4 + 3 = 34 \).

**Step 2: Find the remainder of the sum when divided by 3.**
- We need to find \( 34 \mod 3 \).
- To do this, we can express 34 in terms of multiples of 3:
- \( 34 = 3 \times 11 + 1 \).
- Here, 11 is the quotient and 1 is the remainder.

**Step 3: State the remainder.**
- Therefore, the remainder when 379843 is divided by 3 is **1**.

### Summary of Steps:
1. Sum the digits of the number.
2. Find the remainder of the sum when divided by 3.
3. State the remainder.