Solution: The factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 factors. The probability is $\frac{6}{45} = \frac{2}{15}$. \boxed{\dfrac{2}{15}}

["Understanding the Factors of 45 and Their Probability", "When exploring number properties in mathematics, identifying factors plays a fundamental role — especially in fraction simplification, probability calculations, and divisibility analysis. A particularly simple yet instructive example is the number 45.", "### What Are the Factors of 45?", "The factors of 45 are all the whole numbers that divide 45 evenly without leaving a remainder. These include:\n1, 3, 5, 9, 15, and 45.\nIn total, there are 6 factors, which helps set the stage for probability-based reasoning.", "### Calculating the Probability Using These Factors", "Suppose we consider the probability of randomly selecting one of these factors from all positive integers up to 45. While probability is typically defined over uniform distributions, a meaningful interpretation arises when we compare the count of favorable outcomes (factors of 45) to the total number in our sample set (45):", "- Total factors = 6\n- Total possible values considered = 45", "Thus, the probability is:", "$$\n\frac{\ ext{Number of favorable outcomes}}{\ ext{Total number of outcomes}} = \frac{6}{45}\n$$", "### Simplifying the Probability", "To express this fraction in simplest form:\n$$\n\frac{6}{45} = \frac{2 \ imes 3}{15 \ imes 3} = \frac{2}{15}\n$$", "### Why This Probability Matters", "Understanding such probabilities is essential in:", "- Probability and statistics education\n- Simplifying rational numbers and fractions\n- Teaching divisibility and number theory concepts\n- Building foundational math skills for school and competitive exams", "The simplified probability $\frac{2}{15}$ represents a clear and elegant fraction derived logically from the factorization of 45.", "### Summary", "- Factors of 45: 1, 3, 5, 9, 15, 45 → 6 total factors\n- Probability of selecting a factor of 45 uniformly from 1 to 45 is $\frac{6}{45} = \frac{2}{15}$\n- This example demonstrates how prime factorization supports fraction simplification and probability modeling", "---", "SEO Keywords: factors of 45, probability of factor, simplified fraction 2/15, number theory basics, divisibility examples, fraction probability, math curriculum factors, zero remainder division", "Meta Description: Learn the six factors of 45 and how they form the basis for finding the probability $\frac{6}{45} = \frac{2}{15}$ — a key concept in number theory and fraction simplification."]