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Home » You Won’t Believe How Perfectly Perfect Now’s 8 Inch Cakes Are! - Londonproperty

You Won’t Believe How Perfectly Perfect Now’s 8 Inch Cakes Are! - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Question:** A statistician is modeling data points that follow a discrete probability distribution. What is the probability that a positive integer less than or equal to 60 is a divisor of 120?

📌 Solution:** First, determine how many positive integers \( n \) satisfy \( 1 \leq n \leq 60 \) and \( n \mid 120 \).

📌 First, factor 120:

📌 = 2^3 \cdot 3 \cdot 5

📌 The total number of positive divisors of 120 is:

📌 Now, list all divisors of 120:

📌 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

📌 Among these, the divisors \( \leq 60 \) are all except 120. So there are \( 16 - 1 = 15 \) divisors of 120 that are \( \leq 60 \).

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