Prime Factorisation Worksheets


Factorisation: A number when expressed as a product of its factors is said to be factorised.
For example: 12{\rm{ }} = {\rm{ }}3{\rm{ }} \times {\rm{ }}4 . We say that 12 has been factorised. This is one of the several factorisations of 12.
The others are:
\begin{array}{l}12{\rm{ }} = {\rm{ }}2{\rm{ }} \times {\rm{ }}6\\12{\rm{ }} = {\rm{ }}3{\rm{ }} \times {\rm{ }}4\\12{\rm{ }} = {\rm{ }}1{\rm{ }} \times {\rm{ }}12.\end{array}

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 2{\rm{ }} \times {\rm{ }}2{\rm{ }} \times {\rm{ }}3 . 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:

Thus. 90{\rm{ }} = {\rm{ }}2{\rm{ }} \times {\rm{ }}3{\rm{ }} \times {\rm{ }}3{\rm{ }} \times {\rm{ }}5.

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