# Prime factorisation

Every positive integer is the **product of prime numbers**. The list of prime factors of a number is called its prime factorisation. The prime factorisation of every number is unique.

The number of times that a prime factor appears is its multiplicity.

$$\Tblue{2}$$ has multiplicity $$\Tred{3}$$ in the factorisation of $$24 = \Tblue{2}^\Tred{3} \times \Tgreen{3}$$.

If the prime factorisation of a number is known, it is easy to find **all the factors** of that number. The factors are **all possible products** of the prime factors.

We have the prime factorisation $$$24 = \Tblue{2}^\Tred{3} \times \Tgreen{3}.$$$ So all the factors of $$24$$ are : $$1$$, $$\Tblue{2}$$, $$\Tblue{2}^\Tred{2} = 4$$, $$\Tblue{2}^\Tred{3} = 8$$, $$\Tgreen{3}$$, $$\Tblue{2}\times\Tgreen{3} = 6$$, $$\Tblue{2}^\Tred{2} \times\Tgreen{3} = 12$$ and $$\Tblue{2}^\Tred{3} \times\Tgreen{3} = 24$$.