// Numbas version: finer_feedback_settings
{"name": "19.e. Finding all factors of a number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "19.e. Finding all factors of a number", "tags": [], "metadata": {"description": "<p>Prime factor decomposition starting steps.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Provide all the factors of $\\var{Number}$.</p>", "advice": "<p>For any number $n$ we know 1 and $n$ will always be factors. We will work out the rest of the factors by testing which numbers divide {Number}.</p>\n<p>First try dividing by 2, if this does not work then try 3, then 4 and so on. (In fact, to find the first factor you only need to check the prime numbers 2,3,5,7,...).</p>\n<p>After 1, the first number which divides {Number} is {Factors[1]}. This means that both {Factors[1]} and {Number/Factors[1]} are factors. We can now speed up the process of looking for factors of {Number} by looking for factors of {Number/Factors[1]} instead. Make sure to remember that if $x$ is a factor of {Number/Factors[1]} then both $x$ and $\\var{Factors[1]}\\times x$ are factors of {Number}!</p>\n<p>We only need to look for factors up to $\\sqrt{\\var{Number}}$. Once you have done this you should have the full list of factors {AnswersAsString}.</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Factors\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Number": {"name": "Number", "group": "Ungrouped variables", "definition": "random(1..100)", "description": "<p>All numbers less than 119 have 12 or fewer factors so can't increase this range without increasing the number of options</p>", "templateType": "anything", "can_override": false}, "Factors": {"name": "Factors", "group": "Ungrouped variables", "definition": "divisors(Number)", "description": "", "templateType": "anything", "can_override": false}, "DisplayAnswers": {"name": "DisplayAnswers", "group": "Ungrouped variables", "definition": "if(x<abs(Factors),Factors[x],\"\") for: x of:0..11", "description": "", "templateType": "anything", "can_override": false}, "Temp": {"name": "Temp", "group": "Ungrouped variables", "definition": "if(x=1,\"1\",if(x=\"\",\"\",\", \"+string(x))) for: x of:DisplayAnswers", "description": "", "templateType": "anything", "can_override": false}, "AnswersAsString": {"name": "AnswersAsString", "group": "Ungrouped variables", "definition": "Temp[0]+Temp[1]+Temp[2]+Temp[3]+Temp[4]+Temp[5]+Temp[6]+Temp[7]+Temp[8]+Temp[9]+Temp[10]+Temp[11]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "len(Factors)>2", "maxRuns": 100}, "ungrouped_variables": ["Number", "Factors", "DisplayAnswers", "Temp", "AnswersAsString"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_set (The set of numbers that the student gave):\n  set(x for: x of: interpreted_answers where: x<>nothing)\n\nexpected_set (The set of roots of the equation):\n  set(Factors)\n\nnum_correct (The number of values in the student's set which are correct):\n  len(intersection(student_set, expected_set))\n\nnum_answers: len(expected_set)\n\nnum_incorrect: len(student_set)-num_correct\n\nmark:\n  add_credit(\n    num_correct / num_answers, \"You gave {num_correct} of {num_answers} distinct factors.\")\n  sub_credit(\n    num_incorrect / 12, \"You gave {num_incorrect} answers which are not factors\"\n  )", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Leave boxes empty if there is not enough factors.</p>\n<p>[[0]]</p>\n<p>[[1]]</p>\n<p>[[2]]</p>\n<p>[[3]]</p>\n<p>[[4]]</p>\n<p>[[5]]</p>\n<p>[[6]]</p>\n<p>[[7]]</p>\n<p>[[8]]</p>\n<p>[[9]]</p>\n<p>[[10]]</p>\n<p>[[11]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Gap0", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "student_empty: trim(studentAnswer)=\"\"\n\nmark:  correctif(interpreted_answer in Factors or student_empty)\n//  assert(student_empty, apply(base_mark))\n\ninterpreted_answer:\n  if(student_empty, nothing, base_interpreted_answer)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": 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