Grade 8 Mathematics Assignment Term one 2025 2.4. Rewrite 28 and 72 as a product of their prime factors Determine the HCF and LCM of 28 and 72 D. 2 ,

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**Step 1: Prime Factorisation**

- **For 28:**

Write 28 as a product of primes:
  
  $$
  28 = 2 \times 14 = 2 \times 2 \times 7 = 2^2 \times 7
  $$

- **For 72:**

Write 72 as a product of primes:
  
  $$
  72 = 8 \times 9 = 2^3 \times 3^2
  $$

**Step 2: Find the Highest Common Factor (HCF)**

The HCF is found by taking the product of the common prime factors using the lowest exponents.

- **Common prime factors:**
  
  Both 28 and 72 have the prime factor 2.
  
  - For 28: $$2^2$$
  - For 72: $$2^3$$
  
  The lowest power is $$2^2$$.

Thus,

$$
\text{HCF} = 2^2 = 4
$$

**Step 3: Find the Lowest Common Multiple (LCM)**

The LCM is found by taking the product of all prime factors present in either number using the highest exponents.

- **Prime factors and their highest powers:**

- For 2: Highest power is $$2^3$$ (from 72).
  - For 3: Present only in 72 as $$3^2$$.
  - For 7: Present only in 28 as $$7^1$$.

Thus,

$$
\text{LCM} = 2^3 \times 3^2 \times 7 = 8 \times 9 \times 7 = 504
$$

**Final Answer:**

- Prime factorisation:
  $$
  28 = 2^2 \times 7, \quad 72 = 2^3 \times 3^2
  $$
- HCF: $$4$$
- LCM: $$504$$
**Prime Factorization:** - 28 = 2² × 7 - 72 = 2³ × 3² **HCF:** 4 **LCM:** 504

Grade 8 Mathematics Assignment Term one 2025 2.4. Rewrite 28 and 72 as a product of their prime factors Determine the HCF and LCM of 28 and 72 D. 2 ,

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