Prime numbers and prime factorisation
In a nutshell
Multiplying numbers together forms a product, and this resulting number has factors. Some numbers only have two factors, and these are prime numbers.
Prime numbers
Definition
A prime number is a number that is greater than 1 and has exactly 2 factors: 1 and itself.
The sequence of prime numbers goes as follows:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,...
Prime factorisation
The process of prime factorisation allows you to write any number as a product of its prime factors.
procedure
- Find the smallest prime number which divides the number.
- Write the number as a product of this prime number and the quotient.
- Repeat this process with the quotient until the quotient is a prime number.
- The prime factorisation is the product of all the prime numbers.
Example 1
What is the prime factorisation of 54?
54=27×2
27=9×3
9=3×3
The factors can also been shown using a factor tree:
2◯↙543◯↘↙273◯↘↙9↘3◯
Hence, the prime factorisation of 54 is 54=2×3×3×3=2×33.