Every compound can be broken down uniquely into its elements, but if we are given the elements, there are often a great many different compounds that can be formed from them. In other situations, however, such processes do not work nearly as straightforwardly, as can be illustrated using the analogy of chemistry. (2 × 2) × (3 × 5) = 4 × 15 = 60 or (2 × 5) × (2 × 3) = 10 × 6 = 60Īnd we will always get the same original number, whatever order we choose for multiplying the prime factors. Conversely, if we are given the prime factors of a number, we can reconstruct the original whole number by multiplying the prime factors together, Thus we can factor any whole number into a product of prime numbers, for exampleĪnd this prime factorisation is unique, apart from the order of the factors. A fundamental technique in mathematics is to break something down into its component parts, and rebuild it from those parts.
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