Question
Using prime factorization find the highest common factor of 12,15 and 20
Answers
GPT-4o mini
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**.
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**.