Question

Calculate HCF of 24 and 30

Answer 1

To calculate the Highest Common Factor (HCF) of 24 and 30, we can use the prime factorization method.

1. **Prime factorization of 24:**
- 24 can be factored into \(2 \times 12\)
- 12 can be factored into \(2 \times 6\)
- 6 can be factored into \(2 \times 3\)

So, the prime factorization of 24 is:
\[
24 = 2^3 \times 3^1
\]

2. **Prime factorization of 30:**
- 30 can be factored into \(2 \times 15\)
- 15 can be factored into \(3 \times 5\)

So, the prime factorization of 30 is:
\[
30 = 2^1 \times 3^1 \times 5^1
\]

3. **Identifying common prime factors:**
- The common prime factors of 24 and 30 are \(2\) and \(3\).

4. **Finding the lowest powers of the common factors:**
- For \(2\): the lowest power is \(2^1\)
- For \(3\): the lowest power is \(3^1\)

5. **Calculating the HCF:**
\[
HCF = 2^1 \times 3^1 = 2 \times 3 = 6
\]

Therefore, the HCF of 24 and 30 is **6**.