## What is a prime number?

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that can only be evenly divided by 1 and itself.

For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 are all prime numbers.

On the other hand, 4 is not a prime number because it can be divided by 1, 2, and 4. Similarly, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, and so on are not prime numbers, and are referred to as composite numbers. The number 1 is neither prime nor composite.

Prime numbers have many interesting properties and are important in mathematics and computer science for cryptography, number theory, and other fields.

## What is prime factorization?

Prime factorization is the process of finding the prime numbers that multiply together to give a given number. In other words, it is a way to express a composite number as the product of its prime factors.

To find the prime factorization of a number, you start by dividing the number by the smallest prime number that divides it evenly. Then you repeat this process with the quotient until the quotient is a prime number.

For example, let's find the prime factorization of the number 36:

- Divide 36 by 2, which gives 18. 2 is a prime number.
- Divide 18 by 2, which gives 9. 2 does not divide 9 evenly, so try the next prime number, which is 3.
- Divide 9 by 3, which gives 3. 3 is a prime number.

Therefore, the prime factorization of 36 is 2 ⋅ 2 ⋅ 3 ⋅ 3.

Prime factorization is used in many areas of mathematics, including number theory, cryptography, and algebra. It is also important in computer science for tasks such as integer factorization and prime number generation.

This app uses a fairly simple algorithm to determine whether a number is prime or composite, and if composite, what its prime factors are. As numbers get bigger this becomes a much more difficult task. It becomes so difficult that mathematicians have devised encryption algorithms that rely for their security on the fact that very large numbers are extremely difficult to factor.