1. The problem asks: How many numbers from 50 to 500 have an odd number of factors? 2. Important fact: A number has an odd number of factors if and only if it is a perfect square. This is because factors usually come in pairs, except when the number is a perfect square, where one factor is repeated (the square root). 3. So, we need to count the perfect squares between 50 and 500 inclusive. 4. Find the smallest perfect square greater than or equal to 50: The square root of 50 is approximately $7.07$, so the smallest integer square root is 8. Thus, the smallest perfect square in the range is $8^2 = 64$. 5. Find the largest perfect square less than or equal to 500: The square root of 500 is approximately $22.36$, so the largest integer square root is 22. Thus, the largest perfect square in the range is $22^2 = 484$. 6. Count the perfect squares from $8^2$ to $22^2$: These correspond to the integers 8 through 22 inclusive. 7. The count is $22 - 8 + 1 = 15$. Final answer: There are 15 numbers between 50 and 500 that have an odd number of factors.