Mei Ling has 24 erasers and 36 pencils. She wants to make IDENTICAL gift packs for the school carnival, using ALL the erasers and ALL the pencils with NONE left over. What is the GREATEST number of gift packs she can make?
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Worked Solution
Step 1: Recognise this as a "greatest equal groups" problem → find the GCF of 24 and 36.
Step 2: List the factors. Factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}. Factors of 36 = {1, 2, 3, 4, 6, 9, 12, 18, 36}.
Step 3: Common factors = {1, 2, 3, 4, 6, 12}. The greatest is 12.
Step 4: So Mei Ling can make at most 12 identical packs. Each pack contains: 24 ÷ 12 = 2 erasers and 36 ÷ 12 = 3 pencils. Total used: 12 × 2 = 24 erasers ✓ and 12 × 3 = 36 pencils ✓.
Answer: 12
Correct answer: 12
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