What is the greatest prime factor of 3105?

the answer is simply 23.

Oh, the greatest prime factor of 3105? Well, I have to admit, I'm not a mathematician, but I do know some fun facts. Did you know that the number 3105 can be divided by 5? So, if you're looking for the greatest prime factor, mathematically speaking, it would be 5. But hey, don't take my word for it, I'm just a clown bot trying to bring a smile to your face!

To find the greatest prime factor of 3105, we can use a step-by-step approach.

Step 1: Find the prime factors of 3105.
The prime factors of 3105 are the prime numbers that divide 3105 without leaving a remainder.

Step 2: Divide 3105 by the smallest prime number (2) and continue dividing by the smallest prime number until it is no longer divisible.
3105 ÷ 2 = 1552.5 (not divisible)

Step 3: Move on to the next prime number (3) and continue dividing until it is no longer divisible.
3105 ÷ 3 = 1035

Step 4: Move on to the next prime number (5) and continue dividing until it is no longer divisible.
1035 ÷ 5 = 207

Step 5: Move on to the next prime number (7) and continue dividing until it is no longer divisible.
207 ÷ 7 = 29.571 (not divisible)

Step 6: Continue dividing by larger prime numbers (11, 13, 17, 19, etc.) until it is no longer divisible.
29.571 is not divisible by any prime numbers larger than itself.

Step 7: The highest prime number obtained in the factors is the greatest prime factor of 3105.
In this case, 29 is the greatest prime factor of 3105.

Therefore, the greatest prime factor of 3105 is 29.

To find the greatest prime factor of a number like 3105, we need to factorize it by dividing it by prime numbers until the quotient becomes 1. Let's go through the steps:

1. Start by dividing 3105 by the smallest prime number, which is 2. However, 3105 is not divisible by 2, so we move on to the next prime number.

2. The next prime number is 3. Divide 3105 by 3: 3105 ÷ 3 = 1035. Notice that 1035 is still divisible by 3.

3. Divide 1035 by 3 again: 1035 ÷ 3 = 345. We can divide again because 345 is divisible by 3.

4. Divide 345 by 3 once more: 345 ÷ 3 = 115. At this point, we cannot divide further by 3.

5. Now, let's move on to the next prime number, which is 5. Divide 115 by 5: 115 ÷ 5 = 23. Here we obtained a prime number, which means we have found the prime factors of 3105: 3, 3, 3, 5, and 23.

6. The prime factors of 3105 are 3, 3, 3, 5, and 23. To find the greatest prime factor, we simply look at the largest prime number among these factors. Therefore, the greatest prime factor of 3105 is 23.

So, 23 is the greatest prime factor of 3105.