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Home » Now check if $3^3 = 27$ always divides $P$: - Get link 4share

Now check if $3^3 = 27$ always divides $P$: - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5 clusters: not valid since $12 \div 5 = 2.4$, not an integer

📌 Thus, the largest possible number of regions in each cluster, under the given constraints, is

📌 Question: A science journalist wants to create a data visualization with 180 dots, each representing a unique data point. If each row in the visualization must contain the same number of dots and the number of rows must be a prime number greater than 3, what is the number of rows if the visualization displays the maximum number of dots per row?

📌 Solution: We are given 180 dots and must arrange them into rows with the same number of dots, where the number of rows is a prime number greater than 3. To maximize the number of dots per row, we must minimize the number of rows (among valid prime numbers).

📌 The prime numbers greater than 3 and less than or equal to 180 include: 5, 7, 11, 13, ..., up to 179. We seek the smallest such prime divisor of 180 to maximize dots per row.

📌 First, factor 180:

📌 The prime divisors of 180 are 2, 3, and 5. Among these, the only prime number greater than 3 is 5.

📌 Thus, the only valid prime number of rows greater than 3 that divides 180 is 5. Then the number of dots per row is:

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