Using prime factorization find the highest common factor of 12,15 and 20

Answer 1

To find the highest common factor (HCF) of 12, 15, and 20 using prime factorization, we first need to factor each number into its prime components.

1. Prime factorization of 12:

   • 12 = 2 × 2 × 3 = \(2^2 \times 3^1\)

2. Prime factorization of 15:

   • 15 = 3 × 5 = \(3^1 \times 5^1\)

3. Prime factorization of 20:

   • 20 = 2 × 2 × 5 = \(2^2 \times 5^1\)

Now we list the prime factors:

• 12: \(2^2\), \(3^1\)
• 15: \(3^1\), \(5^1\)
• 20: \(2^2\), \(5^1\)

Next, we identify the common prime factors:

• The only common prime factor among 12, 15, and 20 is \(3^1\).

Now we take the lowest power of the common prime factor:

• The lowest power of 3 present is \(3^0\), as 3 is not a factor of both 20 and 12.

Since there are no other common prime factors (2 and 5 are unique to 12 and 15 respectively), the highest common factor is:

\[ \text{HCF} = 3^0 = 1 \]

Thus, the highest common factor of 12, 15, and 20 is 1.