“ Sure, let's go step by step.
A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. This means if we can find any other number (excluding 1 and the number itself) that divides 17077, then it is not a prime number.
Let's start by checking divisibility by 2. Since 17077 is an odd number (its last digit is 7), it is not divisible by 2.
For the next step, we can look at divisibility by 3. We add up the digits: 1+7+0+7+7 = 22. Because 22 is not divisible by 3, 17077 is also not divisible by 3.
The smallest prime number greater than 3 is 5. Checking divisibility by 5, we see that 17077 does not end in 0 or 5, so it is not divisible by 5.
The smallest prime number greater than 5 is 7. To check divisibility by 7, there is no simple rule like with 2, 3, and 5, so we would perform the actual division. But we can stop here because I just recalled a rule that we can only check up to the square root of the number and the square root of 17077 is approximately 130.68. So if there were factors other than 1 and 17077, we would have found them by now.
Therefore, 17077 is a prime number.”