Question
You are given the following information. \[ 252=2 \times 2 \times 3 \times 3 \times 7 \quad 360=2 \times 2 \times 2 \times 3 \times 3 \times 5 \] 4.3 .1 Determine the bighest common factor (HCF) of 252 and 360 .
Ask by Reed Gough. in South Africa
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The HCF of 252 and 360 is 36.
Solution
To determine the **Highest Common Factor (HCF)** of **252** and **360**, let's analyze their prime factorizations:
\[
\begin{align*}
252 &= 2 \times 2 \times 3 \times 3 \times 7 \quad \text{or} \quad 2^2 \times 3^2 \times 7 \\
360 &= 2 \times 2 \times 2 \times 3 \times 3 \times 5 \quad \text{or} \quad 2^3 \times 3^2 \times 5 \\
\end{align*}
\]
**Steps to find the HCF:**
1. **Identify Common Prime Factors:**
- Both numbers share the prime factors **2** and **3**.
2. **Choose the Lowest Exponent for Each Common Factor:**
- For **2**:
- 252 has \(2^2\)
- 360 has \(2^3\)
- **Choose \(2^2\)**
- For **3**:
- Both have \(3^2\)
- **Choose \(3^2\)**
3. **Multiply the Chosen Factors:**
\[
\text{HCF} = 2^2 \times 3^2 = 4 \times 9 = 36
\]
**Conclusion:**
The **HCF of 252 and 360 is 36**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To find the highest common factor (HCF) of 252 and 360, we first need to identify the common prime factors and take the lowest powers of those factors. The prime factorization of 252 is \(2^2 \times 3^2 \times 7\), and for 360, it's \(2^3 \times 3^2 \times 5\). The common prime factors are \(2\) and \(3\). Now let's take the lowest powers: - For \(2\), the lowest power is \(2^2\). - For \(3\), the lowest power is \(3^2\). Multiply these together to find the HCF: \[ HCF = 2^2 \times 3^2 = 4 \times 9 = 36 \] Thus, the HCF of 252 and 360 is 36.
