Index Notation and Prime Factorisation

Index (Exponential) Notation

Index notation is a way of writing repeated multiplication of the same number.

For example:

\[2\times 2\times 2\times 5\times 5 = 2^3 \times 5^2\]

Prime Factorisation

Prime factorisation means expressing an integer greater than 1 as a product of prime numbers.

Often written using index notation to show repeated factors.

Methods to find prime factors:

Factor tree method: Break down a number step by step until all factors are prime.

Repeated division method (Long division): Divide by the smallest prime repeatedly.