FION 2 Find the HCF of $$ 24 x^{3} y z^{4} ; 30 x^{2} y^{2} z^{3} $$ and $$ 36 x^{3} y^{2} z^{3} $$

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1. **Find the HCF of the numerical coefficients**

- The coefficients are $$24$$, $$30$$, and $$36$$.
   - Prime factorizations:
     - $$24 = 2^3 \times 3$$
     - $$30 = 2 \times 3 \times 5$$
     - $$36 = 2^2 \times 3^2$$
   - Take the minimum power of each common prime:
     - For $$2$$: minimum power is $$2^1$$.
     - For $$3$$: minimum power is $$3^1$$.
   - Therefore, the HCF of the coefficients is:
     $$
     2^1 \times 3^1 = 6
     $$

2. **Find the HCF for the variables**

- For $$x$$:
     - Exponents: $$3$$ (from $$x^3$$), $$2$$ (from $$x^2$$), and $$3$$ (from $$x^3$$).
     - Minimum exponent is $$2$$, so the common factor is $$x^2$$.
   - For $$y$$:
     - Exponents: $$1$$ (from $$y$$), $$2$$ (from $$y^2$$), and $$2$$ (from $$y^2$$).
     - Minimum exponent is $$1$$, so the common factor is $$y$$.
   - For $$z$$:
     - Exponents: $$4$$ (from $$z^4$$), $$3$$ (from $$z^3$$), and $$3$$ (from $$z^3$$).
     - Minimum exponent is $$3$$, so the common factor is $$z^3$$.

3. **Combine the results**

The HCF of the three expressions is:
   $$
   6 x^2 y z^3
   $$
The HCF of $$24x^{3}yz^{4}$$, $$30x^{2}y^{2}z^{3}$$, and $$36x^{3}y^{2}z^{3}$$ is $$6x^{2}yz^{3}$$.

FION 2 Find the HCF of \( 24 x^{3} y z^{4} ; 30 x^{2} y^{2} z^{3} \) and \( 36 x^{3} y^{2} z^{3} \)

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