The smallest number which must be added to 803642 in order to obtain a multiple of 9 is :

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the smallest number that must be added to 803642 in order to obtain a multiple of 9, we can follow these steps:

### Step 1: Calculate the remainder when 803642 is divided by 9.
To determine if a number is a multiple of 9, we can use the divisibility rule for 9, which states that a number is divisible by 9 if the sum of its digits is divisible by 9.

**Calculation of the sum of the digits:**
- The digits of 803642 are: 8, 0, 3, 6, 4, 2.
- Sum = 8 + 0 + 3 + 6 + 4 + 2 = 23.

### Step 2: Find the remainder when the sum of the digits (23) is divided by 9.
Now, we need to find the remainder of 23 when divided by 9.

**Calculation:**
- 23 ÷ 9 = 2 remainder 5.
- Therefore, the remainder is 5.

### Step 3: Determine how much needs to be added to make it a multiple of 9.
To find the smallest number to add, we need to subtract the remainder from 9.

**Calculation:**
- 9 - 5 = 4.

### Conclusion:
The smallest number that must be added to 803642 to make it a multiple of 9 is **4**.

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