Question

Find the greatest common factor. $$412,18$$

Short answer

The greatest common factor of 412 and 18 is \(2\).

Step-by-step solution

Prime Factorization

The prime factorization for the given numbers needs to be found. For \(412\), the prime factors are \(2, 2, 103\) and for \(18\), the prime factors are \(2, 3, 3\).

Finding Common Factors

Looking at the prime factors, the common factor to both \(412\) and \(18\) is \(2\).

Calculation of the GCF

The greatest common factor (GCF) is calculated by multiplying the common prime factors. Since the only common prime factor \(2\) occurs only once in both numbers, the GCF is \(2\).