The least number of five digits which has 123 as a factor is

Options

A. 10037
B. 10086
C. 10081
D. 10063

Answer

To find the least number of five digits which has 123 as a factor, we can follow these steps:

### Step 1: Identify the smallest five-digit number
The smallest five-digit number is 10000.

### Step 2: Divide the smallest five-digit number by 123
Next, we will divide 10000 by 123 to find out how many times 123 fits into 10000 and to determine the remainder.

\[ 10000 \div 123 \approx 81.3008 \]

This means 123 fits into 10000 approximately 81 times.

### Step 3: Calculate the product of 123 and the quotient
Now, we will multiply 123 by the whole number part of the quotient (which is 81) to find the largest multiple of 123 that is less than 10000.

\[ 123 \times 81 = 9963 \]

### Step 4: Find the remainder
Now, we will find the remainder when we subtract this product from 10000.

\[ 10000 - 9963 = 37 \]

### Step 5: Adjust to find the least five-digit number
Since we need a five-digit number, we will add 123 to the product we calculated in Step 3.

\[ 9963 + 123 = 10086 \]

### Conclusion
Thus, the least number of five digits which has 123 as a factor is **10086**.

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