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. You need to think to do it in parallel programming.A fundamental technique in mathematics is to break something down into its component parts, and rebuild it from those parts. In the next section, we will discuss slightly more challenging problem: how to calculate prime factor of any positive integer in Spreadsheet without macro (without do while loop). Input any positive integer number larger than 1: If it is a composite number, the program will list the divisors and gives the prime factorization which is unique for your input number. This interaction program below determines whether your input is a prime or composite number. The flow chart of above algorithm is shown below.Īfter learning about divisors, prime and composite number as well as prime factorization, you may want to try the following online Divisibility-Prime-Factorization calculator. When we use procedural programming, the algorithm of prime factor is as follow The division of 5 with 5 produces 1 and we stop the computation and gathering the result such that 100 = 2 x 2 x 5 x 5 Since 5 is also a prime number, our smallest prime number is We find smallest prime number that actually divides 25 and we found We find smallest prime number that actually divides 50 and again we found We find smallest prime number that actually divides 100 and we found The simplest algorithm to find the prime-factor isīy repeatedly dividing the number with the prime factor until the number becomes 1. Now we proceed with algorithm (method) to compute prime factor manually by hand computation.
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