**Introduction:**
To find the number of even numbers between 540 and 570, we need to identify the even numbers within this range. An even number is any number that is divisible by 2, meaning it has a remainder of 0 when divided by 2. We can determine the number of even numbers in this range by counting them one by one or by using a mathematical formula. Let's explore both methods.

**Method 1: Counting the even numbers individually:**
To find the even numbers between 540 and 570, we can start by listing all the numbers within this range and identifying which ones are even. Here is a breakdown of the numbers in this range:

540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570

By checking each number individually, we can identify the even numbers:

**Even Numbers:**
540, 542, 544, 546, 548, 550, 552, 554, 556, 558, 560, 562, 564, 566, 568, 570

By counting the even numbers, we can conclude that there are 16 even numbers between 540 and 570.

**Method 2: Using a mathematical formula:**
Alternatively, we can use a mathematical formula to determine the number of even numbers between 540 and 570. The formula is as follows:

Number of even numbers = (last number - first number) / 2 + 1

Applying this formula to our problem:

Number of even numbers = (570 - 540) / 2 + 1
= 30 / 2 + 1
= 15 + 1
= 16

Therefore, using the formula, we obtain the same result of 16 even numbers between 540 and 570.

**Conclusion:**
In conclusion, there are a total of 16 even numbers between 540 and 570. We can determine this by either listing and counting the even numbers individually or by using a mathematical formula. Both methods yield the same result.