The manager of a school bookshop received a shipment of 84 pencils. She wants to pack all the pencils into equal groups with no pencils left over. Which of the following CANNOT be the number of groups?
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Worked Solution
Step 1: Understand the condition — the number of groups must be a factor of 84 (divides 84 exactly with no remainder).
Step 2: Test each option by dividing 84 by it.
84 ÷ 6 = 14 (exact, no remainder) → 6 IS a factor.
84 ÷ 9 = 9.33… (remainder of 3) → 9 is NOT a factor.
84 ÷ 12 = 7 (exact, no remainder) → 12 IS a factor.
84 ÷ 14 = 6 (exact, no remainder) → 14 IS a factor.
Answer: 9 cannot be the number of groups because 84 ÷ 9 has a remainder.
Correct answer: 9
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