By which of the following, 555555 is divisible ?

Options

A. 7
B. 11
C. 13
D. None of these

Answer

To determine by which of the following numbers 555555 is divisible, we can follow these steps:

### Step 1: Identify the number
The number we are analyzing is 555555.

### Step 2: Recognize the pattern
The number 555555 can be expressed as a repetition of the digit 5, specifically, it consists of the digit 5 repeated 6 times.

### Step 3: Apply the divisibility rule
There is a known property that states any number formed by repeating a single digit 6 times (like 555555) is divisible by 7, 11, and 13. This is because such numbers can be expressed in the form of \( d \times 111111 \), where \( d \) is the repeated digit.

### Step 4: Check the options
Given the options:
- A) 7
- B) 11
- C) 13
- D) None of these

Since 555555 is divisible by 7, 11, and 13, we can conclude that it is divisible by all three of these numbers.

### Step 5: Determine the correct answer
Since 555555 is divisible by 7, 11, and 13, the correct answer is not "None of these." However, since the question asks for which of the options it is divisible by, we can conclude that the answer is:
- It is divisible by 7, 11, and 13.

### Final Conclusion
The correct answer is that 555555 is divisible by 7, 11, and 13.

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