1. Problem: Does 17 divide each of these numbers? a) 68 b) 84 c) 357 d) 1001 2. To check if 17 divides a number $n$, we verify if $n \mod 17 = 0$. 3. Calculate each remainder: - a) $68 \div 17 = 4$ remainder $\cancel{68}/\cancel{17} = 0$, so 17 divides 68. - b) $84 \div 17 = 4$ remainder $84 - 17 \times 4 = 84 - 68 = 16 \neq 0$, so 17 does not divide 84. - c) $357 \div 17 = 21$ remainder $357 - 17 \times 21 = 357 - 357 = 0$, so 17 divides 357. - d) $1001 \div 17 = 58$ remainder $1001 - 17 \times 58 = 1001 - 986 = 15 \neq 0$, so 17 does not divide 1001. Final answers: - a) Yes - b) No - c) Yes - d) No