An integer is divisible by 16 if and only if its last X digits are divisible by 16. The value of X would be:

Options

A. three
B. four
C. five
D. six

Answer

To determine the value of X such that an integer is divisible by 16 if and only if its last X digits are divisible by 16, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Divisibility by 16**:
- An integer is divisible by 16 if the number can be divided by 16 without leaving a remainder.

2. **Identifying the Power of 2**:
- 16 can be expressed as \(2^4\). This means that for a number to be divisible by 16, it must be divisible by \(2^4\).

3. **Determining the Number of Digits**:
- The divisibility rule for powers of 2 states that for \(2^n\), the last \(n\) digits of the number must be divisible by \(2^n\).
- Since \(16 = 2^4\), we need to check the last 4 digits of the number.

4. **Conclusion**:
- Therefore, the value of X, which represents the number of last digits that must be checked for divisibility by 16, is 4.

### Final Answer:
- The value of X is **4**.