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**. The HCF of 30 and 24 is 6.

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HCF of: - 30 and 24

Ask by Ortiz Harmon. in South Africa

Jan 23,2025

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The HCF of 30 and 24 is 6.

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To find the HCF (Highest Common Factor) of 30 and 24, we can break down the numbers into their prime factors. The prime factorization of 30 is 2 × 3 × 5, while for 24, it's 2 × 2 × 2 × 3. The common prime factors here are 2 and 3. Multiply the smallest powers of these common factors together, which gives us 2¹ × 3¹ = 6. So, the HCF of 30 and 24 is 6! Now, why does knowing the HCF matter? Well, it’s super useful in simplifying fractions! For example, if you wanted to simplify 30/24, knowing that the HCF is 6 helps you divide both the numerator and denominator by 6, giving you 5/4. This small step can help make calculations much easier in math problems or real-world applications like cooking or crafting, where measurements need to be equivalent!

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