Find the nearest number to 56586 which is exactly divisible by 552.

Options

A. 58666
B. 56556
C. 58656
D. 85656

Answer

To find the nearest number to 56,586 that is exactly divisible by 552, we can follow these steps:

### Step 1: Divide 56,586 by 552
First, we need to perform the division of 56,586 by 552 to find the quotient and the remainder.

\[ 56,586 \div 552 \]

### Step 2: Calculate the Quotient
Perform the division:

- 552 goes into 565 (the first three digits of 56,586) once (1).
- Multiply 1 by 552, which gives 552.
- Subtract 552 from 565, resulting in 13.
- Bring down the next digit (8), making it 138.
- 552 goes into 138 zero times (0).
- Bring down the next digit (6), making it 1386.
- 552 goes into 1386 two times (2).
- Multiply 2 by 552, which gives 1104.
- Subtract 1104 from 1386, resulting in 282.

So, the quotient is 102 and the remainder is 282.

### Step 3: Determine the Nearest Numbers
Now that we have the remainder, we can find the nearest numbers that are divisible by 552:

1. **Subtract the remainder from the original number**:
\[ 56,586 - 282 = 56,304 \]

2. **Calculate how much to add to make it divisible**:
\[ 552 - 282 = 270 \]
Then add this to the original number:
\[ 56,586 + 270 = 56,856 \]

### Step 4: Identify the Nearest Number
Now we have two candidates:
- 56,304 (which is 282 less than 56,586)
- 56,856 (which is 270 more than 56,586)

Since we are looking for the nearest number, we compare the distances:
- Distance to 56,304: 282
- Distance to 56,856: 270

Since 270 is less than 282, the nearest number to 56,586 that is exactly divisible by 552 is:

\[ \text{Nearest number} = 56,856 \]

### Final Answer
The nearest number to 56,586 which is exactly divisible by 552 is **56,856**.

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