Find the GCF of 30 and 45

Answer 1

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.