Question

Determine the Highest Common Factor (HCF) of each of the following:
A. 12 ; 18
12 = 2×2×3
18 = 2×3×3
Hcf =?
=?

HCF=?
=?

Answer 1

To find the Highest Common Factor (HCF) of the numbers 12 and 18, we'll first factor each number into its prime components.

For 12:
- The prime factorization is \(12 = 2^2 \times 3^1\).

For 18:
- The prime factorization is \(18 = 2^1 \times 3^2\).

Next, we identify the common prime factors and choose the lowest power of each of these common factors:

1. For the prime factor \(2\):
- The lowest power between \(2^2\) (from 12) and \(2^1\) (from 18) is \(2^1\).

2. For the prime factor \(3\):
- The lowest power between \(3^1\) (from 12) and \(3^2\) (from 18) is \(3^1\).

Now, we multiply these together to find the HCF:
\[
\text{HCF} = 2^1 \times 3^1 = 2 \times 3 = 6.
\]

So, the HCF of 12 and 18 is:
\[
\text{HCF} = 6.
\]