Note: This is a knowledge of number theory question. Do not use a calculator for this question.
Without calculation, explain why Romeo and Juliet can or cannot both be correct when they are talking about the same large number:
Romeo: "The number is 7 × 11 × 17² × 37 × 67 × 97."
Juliet: "The number is 3 × 11 × 21² × 37 × 67 × 89."

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The Answer of Note: This is a knowledge of number theory question. Do not use a calculator for this question. Without calculation, explain why Romeo and Juliet can or cannot both be correct when they are talking about the same large number: Romeo: "The number is 7 × 11 × 17² × 37 × 67 × 97." Juliet: "The number is 3 × 11 × 21² × 37 × 67 × 89."

Note: This Is a Knowledge of Number Theory Question