1. **Problem:** Does 17 divide each of these numbers? a) 68 b) 84 c) 357 d) 1001 2. **Formula and rule:** An integer $a$ divides another integer $b$ (written $a \mid b$) if there exists an integer $k$ such that $b = ak$. 3. **Check each number:** - a) Check if 17 divides 68: $$68 \div 17 = 4$$ Since 4 is an integer, 17 divides 68. - b) Check if 17 divides 84: $$84 \div 17 = \frac{84}{17} \approx 4.941...$$ Not an integer, so 17 does not divide 84. - c) Check if 17 divides 357: $$357 \div 17 = 21$$ Since 21 is an integer, 17 divides 357. - d) Check if 17 divides 1001: $$1001 \div 17 = 58.882...$$ Not an integer, so 17 does not divide 1001. 4. **Final answer:** - 17 divides 68 and 357. - 17 does not divide 84 and 1001.