3 Determine the following from the algebraic terms: \( 30 x^{3} y^{2} z ; \) \( \begin{array}{ll}\text { 3.3.1 } & \text { The prime factors of each term. } \\ 3.3 .2 & \text { The lowest common multiple (LCM) } \\ 3.3 .3 & \text { The highest common factor (HCF) }\end{array} \)

To solve the problem, we will analyze the algebraic term \( 30 x^{3} y^{2} z \) and determine the following: ### 3.3.1 The Prime Factors of Each Term 1. **Numerical Coefficient (30)**: - The prime factorization of \( 30 \) is: \[ 30 = 2 \times 3 \times 5 \] 2. **Variable Factors**: - The variable factors are already in their simplest form: - \( x^{3} \) (which means \( x \) is multiplied by itself 3 times) - \( y^{2} \) (which means \( y \) is multiplied by itself 2 times) - \( z \) (which means \( z \) is multiplied by itself 1 time) Thus, the prime factors of the term \( 30 x^{3} y^{2} z \) are: \[ 2, 3, 5, x, x, x, y, y, z \] ### 3.3.2 The Lowest Common Multiple (LCM) To find the LCM, we consider the prime factors and their highest powers in the term \( 30 x^{3} y^{2} z \): - The LCM will include each prime factor raised to the highest power that appears in the term: - \( 2^{1} \) - \( 3^{1} \) - \( 5^{1} \) - \( x^{3} \) - \( y^{2} \) - \( z^{1} \) Thus, the LCM is: \[ LCM = 2^{1} \times 3^{1} \times 5^{1} \times x^{3} \times y^{2} \times z^{1} = 30 x^{3} y^{2} z \] ### 3.3.3 The Highest Common Factor (HCF) Since we only have one term \( 30 x^{3} y^{2} z \), the HCF is simply the term itself. Thus, the HCF is: \[ HCF = 30 x^{3} y^{2} z \] ### Summary of Results - **Prime Factors**: \( 2, 3, 5, x, x, x, y, y, z \) - **Lowest Common Multiple (LCM)**: \( 30 x^{3} y^{2} z \) - **Highest Common Factor (HCF)**: \( 30 x^{3} y^{2} z \)