Example:
Let's consider the number 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, we can write 12 as:
12 = 1 x 12
12 = 2 x 6
12 = 3 x 4

Factorisation is not unique:
- The factorisation of a number is not unique because different combinations of factors can be multiplied together to obtain the same number.
- In the case of 12, we have multiple ways to factorize it as shown above. This demonstrates that there can be more than one way to express a number as a product of its factors.
- For example, the number 24 can be factorized as:
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
- In each of these cases, we are multiplying different pairs of factors to obtain the number 24. This illustrates that factorisation is not unique, and there can be multiple ways to break down a number into its factors.
- The non-uniqueness of factorisation has important implications in mathematics, particularly in areas such as number theory and algebra where factorisation plays a significant role in solving equations and proving theorems.