what's the prime factorization of 293?

what's the prime factorization of 525?
and factorization of 216?

293 is already a prime number.

Start dividing 525 by 5^2, leaving you with 21. You should recognize the prime factors of that.

Start be dividing 216 by 2^3, leaving you with 27. That looks like 3^3 to me. So the answer in that case is 2^3 * 3^3

To find the prime factorization of a number, you need to break it down into its prime factors, which are the prime numbers that divide the original number evenly.

1. Prime factorization of 293:
To determine if 293 is a prime number, we need to check if it is divisible by any prime numbers up to its square root (√293 ≈ 17.096). Trying prime numbers, we find that 293 is not divisible by 2, 3, 5, 7, 11, 13, or 17. Therefore, 293 is a prime number itself, and its prime factorization is simply 293.

So, the prime factorization of 293 is 293.

2. Prime factorization of 525:
To find the prime factorization of 525, we start by dividing it by the smallest prime number, 2. 525 is an odd number, so it is not divisible by 2. Next, we try 3, which is a prime number and evenly divides 525. The quotient is 175.

Now, we continue by dividing the quotient, 175, by prime numbers starting from 2, 3, 5, and so on. Continuing this process, we find that 175 is divisible by 5, resulting in a quotient of 35.

Next, we divide 35 by 5, and the quotient is 7. Finally, since 7 is a prime number, we cannot divide it further.

Putting it all together, the prime factorization of 525 is 3 * 5 * 5 * 7, or more commonly written as 3 * 5^2 * 7.

So, the prime factorization of 525 is 3 * 5^2 * 7.

3. Factorization of 216:
To factorize 216, we can start by dividing it by small prime numbers until we can no longer divide evenly.

First, we divide 216 by 2, which gives us a quotient of 108. We can divide 108 by 2 again, resulting in a quotient of 54. Continuing this process, we divide 54 by 2, resulting in a quotient of 27.

Next, we try dividing 27 by 3, which is a prime number, and obtain a quotient of 9. Notice that 9 is a perfect square, and since it is divisible by 3, we can divide it by 3 again to get a quotient of 3.

Finally, we reach the prime factorization of 3. Putting it all together, the prime factorization of 216 is 2^3 * 3^3.

So, the prime factorization of 216 is 2^3 * 3^3.