Question
Determine the Highest Common Factor (HCF) of each of the following:
H. 15 ; 30 ; 45
15 = 3 × 5
30 = 2 × 3 × 5
45 = 3 × 3 × 5
HCF=?
=?
H. 15 ; 30 ; 45
15 = 3 × 5
30 = 2 × 3 × 5
45 = 3 × 3 × 5
HCF=?
=?
Answers
GPT-4o mini
To determine the Highest Common Factor (HCF) of the numbers 15, 30, and 45, we first need to find their prime factorizations, which you've already provided:
- \( 15 = 3^1 \times 5^1 \)
- \( 30 = 2^1 \times 3^1 \times 5^1 \)
- \( 45 = 3^2 \times 5^1 \)
Next, we find the HCF by taking the lowest power of each common prime factor:
- For the prime factor **3**, the lowest power is \(3^1\).
- For the prime factor **5**, the lowest power is \(5^1\).
- The prime factor **2** is not common to all three numbers, so we do not include it.
Now we multiply the common prime factors at their lowest powers:
\[
\text{HCF} = 3^1 \times 5^1 = 3 \times 5 = 15
\]
Thus, the HCF of 15, 30, and 45 is \( \boxed{15} \).
- \( 15 = 3^1 \times 5^1 \)
- \( 30 = 2^1 \times 3^1 \times 5^1 \)
- \( 45 = 3^2 \times 5^1 \)
Next, we find the HCF by taking the lowest power of each common prime factor:
- For the prime factor **3**, the lowest power is \(3^1\).
- For the prime factor **5**, the lowest power is \(5^1\).
- The prime factor **2** is not common to all three numbers, so we do not include it.
Now we multiply the common prime factors at their lowest powers:
\[
\text{HCF} = 3^1 \times 5^1 = 3 \times 5 = 15
\]
Thus, the HCF of 15, 30, and 45 is \( \boxed{15} \).