How many numbers, lying between 1 and 500, are divisible by 13?

Step 1: Find the first number divisible by 13 within the range. The first number greater than 1 that is divisible by 13 is 13 itself.

Step 2: Find the last number divisible by 13 within the range. The largest number less than 500 that is divisible by 13 is 494.

Step 3: Calculate how many numbers are between 13 and 494 that are divisible by 13.

To do this, divide the last number by 13 and the first number by 13, then subtract the two results.

494/13 = 38 13/13 = 1

38 - 1 = 37

Step 4: Add 1 to the result because both 13 and 494 are included in the range.

37 + 1 = 38

So, there are 38 numbers between 1 and 500 that are divisible by 13.