Find the HCF of the following :
`26x^(2)y^(2)z^(2)` and `39x^(3)y^(2)z`

Answer

To find the Highest Common Factor (HCF) of the expressions \( 26x^{2}y^{2}z^{2} \) and \( 39x^{3}y^{2}z \), we can follow these steps:

### Step 1: Factor the coefficients
First, we need to factor the numerical coefficients of the two expressions.

- The coefficient of the first expression \( 26 \) can be factored as:
\[ 26 = 2 \times 13 \]

- The coefficient of the second expression \( 39 \) can be factored as:
\[ 39 = 3 \times 13 \]

### Step 2: Identify the common factors of the coefficients
Now, we look for the common factors in the coefficients \( 26 \) and \( 39 \):
- The common factor is \( 13 \).

### Step 3: Factor the variables
Next, we need to consider the variable parts of the expressions:
- For \( 26x^{2}y^{2}z^{2} \), the variable part is \( x^{2}y^{2}z^{2} \).
- For \( 39x^{3}y^{2}z \), the variable part is \( x^{3}y^{2}z \).

### Step 4: Identify the common factors of the variables
Now, we find the common factors for each variable:
- For \( x \): The minimum power is \( x^{2} \) (from \( x^{2} \) and \( x^{3} \)).
- For \( y \): The minimum power is \( y^{2} \) (from both \( y^{2} \)).
- For \( z \): The minimum power is \( z^{1} \) (from \( z^{2} \) and \( z^{1} \)).

### Step 5: Combine the common factors
Now we can combine the common factors we found:
- The HCF of the coefficients is \( 13 \).
- The HCF of the variable parts is \( x^{2}y^{2}z^{1} \).

Thus, the HCF of the two expressions is:
\[ HCF = 13x^{2}y^{2}z \]

### Final Answer
The HCF of \( 26x^{2}y^{2}z^{2} \) and \( 39x^{3}y^{2}z \) is:
\[ \boxed{13x^{2}y^{2}z} \]