Find the number of possible HCF values for N, N + 25?

Options

A. A)2
B. B)3
C. C)4
D. D)5

Answer

To find the number of possible HCF (Highest Common Factor) values for the numbers \( N \) and \( N + 25 \), we can follow these steps:

### Step 1: Understand the relationship between \( N \) and \( N + 25 \)
The two numbers are \( N \) and \( N + 25 \). The HCF of these two numbers can be expressed in terms of their difference.

### Step 2: Calculate the difference
The difference between \( N + 25 \) and \( N \) is:
\[ (N + 25) - N = 25 \]

### Step 3: Use the property of HCF
According to the property of HCF, we know that:
\[ \text{HCF}(N, N + 25) = \text{HCF}(N, 25) \]
This means that the HCF of \( N \) and \( N + 25 \) is the same as the HCF of \( N \) and the difference (which is 25).

### Step 4: Determine the factors of 25
Next, we need to find the factors of 25 to determine the possible HCF values. The factors of 25 are:
\[ 1, 5, 25 \]

### Step 5: Conclusion
Thus, the possible HCF values for \( N \) and \( N + 25 \) are the factors of 25. Therefore, the number of possible HCF values is:
\[ \text{Total possible HCF values} = 3 \]

### Final Answer
The number of possible HCF values for \( N \) and \( N + 25 \) is **3**.

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