If H.C.F. of x and y is z, then H.C.F. of `(x)/(z)and(y)/(z)` is :

Options

A. x
B. z
C. y
D. 1

Answer

To solve the problem, we need to find the H.C.F. (Highest Common Factor) of the fractions \( \frac{x}{z} \) and \( \frac{y}{z} \), given that the H.C.F. of \( x \) and \( y \) is \( z \).

### Step-by-step Solution:

1. **Understanding the Given Information**:
- We know that \( \text{H.C.F.}(x, y) = z \).
- This means that \( z \) is the largest number that divides both \( x \) and \( y \) without leaving a remainder.

2. **Expressing the H.C.F. of the Fractions**:
- We need to find \( \text{H.C.F.}\left(\frac{x}{z}, \frac{y}{z}\right) \).
- According to the property of H.C.F., we can express this as:
\[ \text{H.C.F.}\left(\frac{x}{z}, \frac{y}{z}\right) = \frac{\text{H.C.F.}(x, y)}{\text{L.C.M.}(z, z)} \]

3. **Finding the H.C.F. and L.C.M.**:
- We already know that \( \text{H.C.F.}(x, y) = z \).
- Now, we need to calculate \( \text{L.C.M.}(z, z) \). The L.C.M. of any number with itself is the number itself:
\[ \text{L.C.M.}(z, z) = z \]

4. **Substituting Values**:
- Now substituting these values back into our expression:
\[ \text{H.C.F.}\left(\frac{x}{z}, \frac{y}{z}\right) = \frac{z}{z} \]

5. **Simplifying the Expression**:
- Simplifying \( \frac{z}{z} \) gives us:
\[ \text{H.C.F.}\left(\frac{x}{z}, \frac{y}{z}\right) = 1 \]

### Final Answer:
Thus, the H.C.F. of \( \frac{x}{z} \) and \( \frac{y}{z} \) is **1**.

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