Prime, Composite, Square, & Prime Factorization

When dealing with numbers, you can classify them into many different categories. In this post, we are going to look at the categories of prime, composite, and square. We will also take a look at prime factorization, which although is not a category for placing numbers, it will help you see the make up of the composite numbers.

Prime numbers are numbers that are only divisible by one and itself. Some examples of prime numbers are 2, 3, 5, 7, and 9. There are many more prime numbers, but that should give you a good look at what some are.

Composite numbers are numbers that are divisible by sets other than just one and itself. They are the exact opposite of a prime number. For example, 4 would be a composite number because it's factors are 1 times 4 and 2 times 2. As you can see, there is more than one way to divide this number to get a whole number. Other examples of composite numbers would be 6, 8, 9, and 10, and the list goes on and on.

Square numbers are numbers where a number is multiplied by itself to get the product. If you were to take the square root of a square number, you would get a solid whole number. For example, 4 would be a square number because it is the product of 2 times 2. Some other examples of square numbers would be 9, 16, 25, and 36. As you can see, square numbers are also classified as composite numbers, because they have more than one set of numbers that can be multiplied into and divided out of them.

Prime Factorization is a unique way to write out a number. There are no two numbers that have the same prime factorization. An example of a prime factorization we could look at would be for the number 48. We start by breaking 48 down into all the prime numbers that go into it. So if we start at the first prime (2), 48 divided by 2 is 24. Divide that answer by 2 again, and you get 12. You can divide that number by 2 as well and you would then have 6. You can divide that by 2 and your answer would be 3. So the prime factorization for the number 48 would be 2x2x2x2x3, or otherwise known as 2^4 (two to the fourth power) times 3. The prime factorization of a number shows the quantity of prime numbers you multiply together to get to the original number.