Question
Determine the Highest Common Factor (HCF) of each of the following:
A. 72 ; 108
72 = 2×2×2×3×3
108 = 2×2×3×3×3
Hcf =?
=?
HCF=?
=?
A. 72 ; 108
72 = 2×2×2×3×3
108 = 2×2×3×3×3
Hcf =?
=?
HCF=?
=?
Answers
GPT-4o mini
To find the Highest Common Factor (HCF) of the numbers 72 and 108, we can use their prime factorization.
**Prime factorization:**
- 72 = \(2^3 \times 3^2\)
- 108 = \(2^2 \times 3^3\)
Now, to find the HCF, we take the lowest power of each common prime factor.
**Common prime factors and their minimum powers:**
- For \(2\): The minimum power is \(2^2\) (from 108).
- For \(3\): The minimum power is \(3^2\) (from 72).
Now, we multiply these together to find the HCF:
\[
\text{HCF} = 2^2 \times 3^2 = 4 \times 9 = 36
\]
Therefore, the Highest Common Factor (HCF) of 72 and 108 is **36**.
**Prime factorization:**
- 72 = \(2^3 \times 3^2\)
- 108 = \(2^2 \times 3^3\)
Now, to find the HCF, we take the lowest power of each common prime factor.
**Common prime factors and their minimum powers:**
- For \(2\): The minimum power is \(2^2\) (from 108).
- For \(3\): The minimum power is \(3^2\) (from 72).
Now, we multiply these together to find the HCF:
\[
\text{HCF} = 2^2 \times 3^2 = 4 \times 9 = 36
\]
Therefore, the Highest Common Factor (HCF) of 72 and 108 is **36**.