Find the least number which should be subtracted from 9999 so that the difference is exactly divisible by 16 ?

Options

A. 15
B. 12
C. 14
D. 13

Answer

To find the least number that should be subtracted from 9999 so that the difference is exactly divisible by 16, we can follow these steps:

### Step 1: Find the remainder when 9999 is divided by 16
To determine how much we need to subtract from 9999, we first need to find the remainder of 9999 when divided by 16.

**Calculation:**
9999 ÷ 16 = 624 with a remainder of 15.

So, \( 9999 \mod 16 = 15 \).

### Step 2: Determine the number to subtract
To make the difference divisible by 16, we need to subtract the remainder (which is 15) from 9999.

**Calculation:**
The least number to subtract = Remainder = 15.

### Step 3: Verify the result
Now, let's verify if subtracting 15 from 9999 gives a number that is divisible by 16.

**Calculation:**
9999 - 15 = 9984.

Now, we check if 9984 is divisible by 16:

9984 ÷ 16 = 624 (which is a whole number).

### Conclusion
Thus, the least number that should be subtracted from 9999 to make the result exactly divisible by 16 is **15**.

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