29:null 2a:["$","title",null,{"children":"Prime factorization (Prime numbers) | Christophe Yamahata | Observable"}] 2f:T550,{ var size = array_primeFactors.length; var result_1 = '', result_2 = ''; var power = 1; var use_power = false; var times = ''; // Display result no.1; result_1 = array_primeFactors[size-1].toString().concat(result_1); for(let i= size-2; i>=0; i--){ result_1 = array_primeFactors[i].toString().concat(' × ',result_1); } // Display result no.2; for(let i= size-1; i>=0; i--){ if(array_primeFactors[i]==array_primeFactors[i-1]){ power += 1; use_power = true; } else { if(power==1) {power="";} // We don't display "^1" if(result_2 != '') { times = ' × ';} // Condition is fulfilled to add the times (×) symbol. result_2 = array_primeFactors[i].toString().concat('^',power,'',times,result_2); power = 1; // Reinitialize power to 1 } } if(size>1){ return html`Its prime factorization can be written as follows:
n = ${integer} = ${use_power == false? ` ${result_1}.

` : `${result_1}
In a compact form, it becomes:
n = ${integer} = ${result_2}.

` } `; } else{ return html `
`; } }30:[] 2d:{"id":"5e6a7492877ceb2e","slug":"prime-factorization","title":"Prime factorization (Prime numbers)","thumbnail":"3c74d7832ef1930b40b17a97144bc68a39c878b96decbc854cad6f340035c66e","access_level":"public","create_time":"$D2022-08-11T14:37:46.912Z","update_time":"$D2024-08-07T17:31:11.967Z","view_time":null,"first_public_time":"$D2022-08-11T21:44:16.890Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":"starter_2024"},"version":791,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"06f083eba60f5a76","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":null}],"members":[{"type":"individual","id":"06f083eba60f5a76","login":"christophe-yamahata","name":"Christophe Yamahata","avatar_url":"https://avatars-next.observableusercontent.com/8256ac716aa8395babba412b2835913d186874fa4190df57a4a28f2e60129876","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":{"id":"19262496cb287a16","slug":"mathematics","title":"Mathematics","owner":{"id":"dd67891d326bcfb1","login":"christophe-yamahata","name":"Christophe Yamahata"}},"type":"notebook","body":{"title":"Prime factorization (Prime numbers)","cells":[{"id":0,"value":"# Prime factorization (Prime numbers)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":623,"value":"

In this notebook, we compute the prime factors of the following natural number \n
(for another number, click on the slider or enter a new value 1 ≤ n ≤ ${max_number} ):

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":215,"value":"viewof integer = Inputs.range([1, max_number], {value: initial_value, step: 1, label: \"Natural number, n:\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":339,"value":"{\n var prime_number = \"\";\n if(integer>1 && array_primeFactors.length==1) {\n prime_number = \"is a prime number.

A natural number n is a prime number (or prime) if it is ≥ 2 and cannot be written as the product of two smaller natural numbers. The first 25 prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

\";\n } else {\n prime_number = \"is not a prime number.\";\n }\n return html`The natural number n = ${integer} ${prime_number}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":237,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":521,"value":"---\n To perform this prime factorization, we use the following javascript function: \n ```js \n // Find the prime factors of the natural number 'n'\n function primeFactors(n) {\n\n if (n<2) { return [n]; } // For n = 0 or n = 1, we return an array with only one row: [n]\n \n const factors = [];\n let divisor = 2;\n \n while (n >= 2) {\n if (n % divisor == 0) {\n factors.push(divisor);\n n = n / divisor;\n } else {\n divisor++;\n }\n }\n return factors; \n }\n ``` ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":656,"value":"
","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":570,"value":"This function returns an array that can easily be manipulated to display the prime factorization: \n ```js \n primeFactors(${integer}) = ▶ Array(${array_primeFactors.length}) [${ [array_primeFactors] }]\n ```","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":330,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":232,"value":"initial_value = 34866","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":769,"value":"max_number = 9999999+1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"array_primeFactors = primeFactors(integer)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"// See also: \n// https://stackoverflow.com/questions/39899072/how-can-i-find-the-prime-factors-of-an-integer-in-javascript\n//\n// Find the prime factors of the natural number 'n'\nfunction primeFactors(n) {\n\n if (n<2) { return [n]; } // For n = 0 or n = 1, we return an array with only one row: [n]\n\n const factors = [];\n let divisor = 2;\n\n while (n >= 2) {\n if (n % divisor == 0) {\n factors.push(divisor);\n n = n / divisor;\n } else {\n divisor++;\n }\n }\n return factors; \n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2e:"$2d:body"