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Roots of a Number Long Multiplication Graphing Slope, Undefined Slope, Flat Slope Square Root Rules Apothem Line Decimal Place Value Multiplying and Dividing Radical TermsFinding Prime Factors

A prime factor, is simply a factor of a number, that happens to be prime.

Finding prime factors of a non prime number, is similar to trying to find general __ factors__
of a number.

Except that we’re specifically looking for factors that are prime numbers.

With prime factorization, we aim to re-write a number as the product of prime factors multiplied together.

We can start by just looking at a random number for an example, let’s say **56**.

The approach for prime factorization of **56**, is to keep dividing by prime numbers, until the
answer of the division ends up being a prime number.

Look to start off by trying to divide by the lowest prime number there is, which is **2**.

**7** is a prime number, so we can stop the division here.

**Next
Step**

Now, the different prime numbers that are used to divide at each stage, should give back the
original number that was started with.

If multiplied together with the last prime number obtained after division was stopped.

In this case with **56**, it wasn't different prime numbers used, as it was only **2** that
was used in division at each stage.

But **2** was still used a total of  3 times before we eventually obtained the prime
number of **7**.

So we do:

This sum form can be simplified with an exponent/power, to result in.

In this form, **2** and **7** are factors that are prime.

That completes the prime factorization of **56**.

Let’s try prime factorization and finding prime factors again, this time with **45**.

Again, starting division with **2** first.

First attempt doesn’t give a whole number, so try to start with the next prime number instead,
**3**.

This can be written as **3**^{2}
× **5** = **45**.

Which is the prime factorization for **45**.

Below is a chart of prime numbers up to  500.

A larger list of prime numbers can be seen on the __ prime
numbers introduction__ page.

When learning about prime factors and finding prime factors, it's also handy to learn about something
called the "fundamental theorem of arithmetic".

The theorem states that every positive integer greater than **1** is either:

- A prime number.

- A non prime number that can be formed by multiplying prime numbers together.

This fundamental theorem of arithmetic can also be called the "unique factorization theorem".

The first six prime numbers are:

The numbers in between are:

These in between numbers can be formed by multiplying prime numbers together.

And so on.

We can try this with any positive integer.

The theorem also states that the set of prime numbers that do multiply together to give a non prime
number, will be unique.

So for **51** and **60** above, the prime multiplications shown, are the only ones
containing prime numbers that will give **51** and **60**.

So a different order of numbers doesn’t mean two different sets of numbers.

The multiplication

They are the same prime multiplication.

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