Factorisation: A number when expressed as a product of its factors is said to be factorised.
For example: . We say that 12 has been factorised. This is one of the several factorisations of 12.
The others are:
Prime Factorisation: It is the ultimate factorisation of a given number. Moreover, it is unique (exactly one).
For example: While factorising 12, we ultimately reach the unique factorisation . In this factorisation, the only factors 2 and 3 are prime numbers. Such a factorisation of a number is called prime factorisation of that number. Thus, 2 × 2 × 3 is the only prime factorisation of 12.
Factor tree: When we go on factorizing a number till, we reach its ultimate factorisation and write the process as follows, we get the shape of a tree called Factor tree.
For example: Let us factorize 90. Let us see below: