Asked by Brianna sapp
Find the GCF of 30 and 45
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of 30 and 45, we can start by determining the prime factorization of each number.
1. **Prime Factorization:**
- For **30**:
- \(30 = 2 \times 3 \times 5\)
- For **45**:
- \(45 = 3^2 \times 5\)
2. **Identify the common factors**:
The prime factors of 30 are \(2\), \(3\), and \(5\). The prime factors of 45 are \(3\) and \(5\). The common prime factors are \(3\) and \(5\).
3. **GCF Calculation**:
- The lowest powers of the common factors:
- For \(3\), the minimum power is \(1\) (from 30).
- For \(5\), the minimum power is \(1\) (both have \(5^1\)).
Therefore, the GCF is:
\[
GCF = 3^1 \times 5^1 = 3 \times 5 = 15
\]
Thus, the GCF of 30 and 45 is **15**.
1. **Prime Factorization:**
- For **30**:
- \(30 = 2 \times 3 \times 5\)
- For **45**:
- \(45 = 3^2 \times 5\)
2. **Identify the common factors**:
The prime factors of 30 are \(2\), \(3\), and \(5\). The prime factors of 45 are \(3\) and \(5\). The common prime factors are \(3\) and \(5\).
3. **GCF Calculation**:
- The lowest powers of the common factors:
- For \(3\), the minimum power is \(1\) (from 30).
- For \(5\), the minimum power is \(1\) (both have \(5^1\)).
Therefore, the GCF is:
\[
GCF = 3^1 \times 5^1 = 3 \times 5 = 15
\]
Thus, the GCF of 30 and 45 is **15**.
There are no human answers yet. A form for humans to post answers is coming very soon!