Continue until all numbers are either circled or crossed out.Circle the next number not crossed out (which is 3), and then cross out multiples of 3.Circle the next number 2, and then cross out every multiple of 2.Cross out 0 and 1 - they are exceptions.Write down all the whole numbers up to 100.Here is a systematic way of writing down all the prime numbers, and all the composite numbers, up to 100. It is better to be precise than to invite arguments about what may be implied, but unsaid. Students often realise that a prime number like 5 has other factors if larger number systems are considered, for example, The phrase ‘whole number factor’ makes the restriction in the definitions quite clear. The number system we are talking about is the set of whole numbers 0, 1, 2, 3, …, and The phrase also excludes 0, which is divisible by every whole number and so has no sensible prime factorisation. The phrase ‘greater than 1’ is needed in the definition of composite numbers to exclude 1, which has no prime factors and so is not the product of two or more prime numbers. We do not want 1 to be a prime number, otherwise the factorisation of numbers into primes would not be unique. The phrase ‘greater than 1’ is needed in the definition of prime numbers to exclude 1. A composite number is a whole number greater than 1 that is not a prime number.A prime number is a whole number greater than 1 whose only whole number factors are itself and 1.’.Prime numbers and composite numbers need to be defined rather carefully: the composite numbers 4, 6, 8, 9, 10, …, which can be factored into the product.the prime numbers 2, 3, 5, 7, 11, …, which cannot be factored into smaller numbers,.
We leave aside the numbers 0 and 1, and then organise the remaining whole numbers 2, 3, 4, 5, … into: The discussion above shows that for the purposes of prime factorisation, we need to distinguish three types of whole numbers. Prime factorisation is a very useful tool when working with whole numbers, and will be used in mental arithmetic, in fractions, for finding square roots, and in calculating the HCF and LCM. 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. This includes a human posting the output of a bot, such as ChatGPT.īlockchain posts must be tagged Blockchain posts are allowed as long as they are related to Haskell, but they must use the "blockchain" tag.A fundamental technique in mathematics is to break something down into its component parts, and rebuild it from those parts. They will be banned with extreme prejudice. Bots cannot be used to make posts or comments. Simply looking for people with interest in or experience with Haskell is not sufficient. Job postings are allowed as long as the job actually involves working with Haskell. Questions about homework are fine, but this subreddit is not here to do your homework for you. Both asking and answering homework questions is not allowed. No matter how funny, memes and image macros are not allowed. Posts about topics that are adjacent to Haskell, like for example functional programming, are typically allowed. For example a post about OCaml would only be allowed if there was a connection to Haskell. Top-level posts should be primarily about Haskell. The Haskell programming language community.ĭaily news and info about all things Haskell related: practical stuff, theory, types, libraries, jobs, patches, releases, events and conferences and more.
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