HCF of: - 30 and 24

To find the Highest Common Factor (HCF) of **30** and **24**, you can use the **prime factorization** method or the **Euclidean algorithm**. Here's how you can do it using both methods: --- ### **Method 1: Prime Factorization** 1. **Find the prime factors of each number:** - **30:** \[ 30 = 2 \times 3 \times 5 \] - **24:** \[ 24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3 \] 2. **Identify the common prime factors:** - Both numbers have the prime factors **2** and **3** in common. 3. **Multiply the smallest powers of the common prime factors:** - For **2**, the smallest power is \(2^1\). - For **3**, the smallest power is \(3^1\). \[ \text{HCF} = 2^1 \times 3^1 = 2 \times 3 = 6 \] --- ### **Method 2: Euclidean Algorithm** The Euclidean algorithm is a systematic method for finding the HCF of two numbers. 1. **Divide the larger number by the smaller number and find the remainder:** \[ 30 \div 24 = 1 \text{ with a remainder of } 6 \] 2. **Replace the larger number with the smaller number and the smaller number with the remainder:** Now, find the HCF of **24** and **6**. 3. **Repeat the process:** \[ 24 \div 6 = 4 \text{ with a remainder of } 0 \] 4. **When the remainder is 0, the smaller number is the HCF:** \[ \text{HCF} = 6 \] --- ### **Conclusion** The **Highest Common Factor (HCF)** of **30** and **24** is **6**.