What smallest number should be subtracted from 9805 so that it is divisible by 8?

Options

A. 3
B. 4
C. 5
D. 7

Answer

To find the smallest number that should be subtracted from 9805 so that it becomes divisible by 8, we can follow these steps:

### Step 1: Determine the remainder when 9805 is divided by 8.
To do this, we perform the division:

1. Divide 9805 by 8.
2. Calculate how many times 8 fits into 9805.

### Step 2: Perform the division.
- 8 goes into 98 (the first two digits of 9805) 12 times because \(8 \times 12 = 96\).
- Subtract 96 from 98, which gives us a remainder of 2.
- Bring down the next digit (0), making it 20.
- 8 goes into 20 two times because \(8 \times 2 = 16\).
- Subtract 16 from 20, which gives us a remainder of 4.
- Bring down the last digit (5), making it 45.
- 8 goes into 45 five times because \(8 \times 5 = 40\).
- Subtract 40 from 45, which gives us a remainder of 5.

Thus, the remainder when 9805 is divided by 8 is 5.

### Step 3: Calculate the smallest number to subtract.
To make 9805 divisible by 8, we need to subtract the remainder (which is 5) from 9805.

### Step 4: Conclusion
Therefore, the smallest number that should be subtracted from 9805 to make it divisible by 8 is **5**.

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