Question
Find the HCF of 36 72
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GPT-4o mini
To find the highest common factor (HCF) of 36 and 72, we can list the factors of each number and then identify the largest common factor.
**Factors of 36:**
- 1, 2, 3, 4, 6, 9, 12, 18, 36
**Factors of 72:**
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Now, let's identify the common factors:
- Common factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
The highest common factor is **36**.
You can also find the HCF using the prime factorization method:
1. **Prime factorization of 36:**
- 36 = 2^2 × 3^2
2. **Prime factorization of 72:**
- 72 = 2^3 × 3^2
3. **Taking the lowest power of the common prime factors:**
- For 2, the lowest power is 2 (from \(2^2\)).
- For 3, the lowest power is 2 (from \(3^2\)).
So, HCF = \(2^2 × 3^2 = 4 × 9 = 36\).
Thus, the HCF of 36 and 72 is **36**.
**Factors of 36:**
- 1, 2, 3, 4, 6, 9, 12, 18, 36
**Factors of 72:**
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Now, let's identify the common factors:
- Common factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
The highest common factor is **36**.
You can also find the HCF using the prime factorization method:
1. **Prime factorization of 36:**
- 36 = 2^2 × 3^2
2. **Prime factorization of 72:**
- 72 = 2^3 × 3^2
3. **Taking the lowest power of the common prime factors:**
- For 2, the lowest power is 2 (from \(2^2\)).
- For 3, the lowest power is 2 (from \(3^2\)).
So, HCF = \(2^2 × 3^2 = 4 × 9 = 36\).
Thus, the HCF of 36 and 72 is **36**.
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