Find the smallest four-digit number that is divisible by 47.
(a)1200
(b)1025
(c)1360
(d)1034

Options

A. 1200
B. 1025
C. 1360
D. 1034

Answer

To find the smallest four-digit number that is divisible by 47, we can follow these steps:

### Step 1: Identify the smallest four-digit number
The smallest four-digit number is 1000.

### Step 2: Divide 1000 by 47
We need to determine how many times 47 fits into 1000. We perform the division:
\[ 1000 \div 47 \approx 21.2766 \]
This means 47 fits into 1000 approximately 21 times.

### Step 3: Multiply 47 by the whole number part of the division
Now, we multiply 47 by 21 to find the largest multiple of 47 that is less than 1000:
\[ 47 \times 21 = 987 \]

### Step 4: Calculate the remainder
Next, we calculate the remainder when 1000 is divided by 47:
\[ 1000 - 987 = 13 \]
This means that 1000 is 13 more than the last multiple of 47.

### Step 5: Determine how much more is needed to reach the next multiple of 47
To find the next multiple of 47, we need to add the difference between 47 and the remainder:
\[ 47 - 13 = 34 \]

### Step 6: Add this difference to 1000
Now, we add this difference to 1000 to find the smallest four-digit number that is divisible by 47:
\[ 1000 + 34 = 1034 \]

### Conclusion
Thus, the smallest four-digit number that is divisible by 47 is **1034**.

### Answer
(d) 1034

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