Two boxes of cookies contain 84 and 126 cookies respectively. The cookies from BOTH boxes are to be packed into identical small bags such that each bag has the same number of cookies, and the bags use up ALL the cookies (no leftovers). What is the GREATEST number of cookies per bag?
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Worked Solution
Step 1: Find the HCF (highest common factor) of 84 and 126.
84 = 2² × 3 × 7. 126 = 2 × 3² × 7.
Step 2: HCF = 2 × 3 × 7 = 42.
Step 3: Each bag has 42 cookies (84 ÷ 42 = 2 bags from box 1; 126 ÷ 42 = 3 bags from box 2).
Answer: 42
Correct answer: 42
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