Numbers divisible by 6

1. A number \( n \) is divisible by \( 6 \) if it can be written as \[ n = 6k \] where \( k \) is an integer. 2. Divisibility by \( 6 \) means that \( n \) must be divisible by both \( 2 \) and \( 3 \). - A number is divisible by \( 2 \) if its last digit is even. - A number is divisible by \( 3 \) if the sum of its digits is divisible by \( 3 \). 3. For example, consider \( n = 24 \): - \( 24 \) is even, so it is divisible by \( 2 \). - The sum of the digits of \( 24 \) is \( 2 + 4 = 6 \), and \( 6 \) is divisible by \( 3 \). Since \( 24 \) meets both criteria, it is divisible by \( 6 \). We can also write \[ 24 = 6 \times 4. \] 4. In conclusion, the numbers divisible by \( 6 \) are of the form \[ \{ n \mid n = 6k, \, k \in \mathbb{Z} \}. \] Any such number fulfills the conditions for divisibility by \( 6 \).