// Numbas version: exam_results_page_options
{"name": "Finding the highest common factor of two numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variable_groups": [], "name": "Finding the highest common factor of two numbers", "functions": {}, "rulesets": {}, "ungrouped_variables": ["sixfac", "fourfac", "hc"], "metadata": {"description": "<p>This question tests the student's ability to identify the factors of some composite numbers and the highest common factors of two numbers.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<h4>a)</h4>\n<p><em>i) </em></p>\n<p>$\\var{fourfac}$ has four factors: $1$, $3$, $\\var{fourfac/3}$ and $\\var{fourfac}$.&nbsp;</p>\n<p>It is possible to pair the factors up to prove that they are factors.&nbsp;</p>\n<p>\\[ <br/>\\begin{align}<br/>1\\times\\var{fourfac}&amp;=\\var{fourfac}\\text{.}\\\\<br/>3\\times\\var{fourfac/3}&amp;=\\var{fourfac}\\text{.}\\\\<br/>\\end{align}<br/>\\]</p>\n<p><em>ii)</em></p>\n<p>$\\var{sixfac}$ has six factors: $1$, $2$, $3$, $\\var{sixfac/3}$, $\\var{sixfac/2}$ and $\\var{sixfac}$.</p>\n<p>Again, it is possible to pair the factors up to prove that they are factors.&nbsp;</p>\n<p>\\[ <br/>\\begin{align}<br/>1\\times\\var{sixfac}&amp;=\\var{sixfac}\\text{.}\\\\<br/>2\\times\\var{sixfac/2}&amp;=\\var{sixfac}\\text{.}\\\\<br/>3\\times\\var{sixfac/3}&amp;=\\var{sixfac}\\text{.}\\\\<br/>\\end{align}<br/>\\]</p>\n<p></p>\n<h4></h4>\n<h4>b)</h4>\n<p>We now&nbsp;look for common factors between the two lists of factors, and the highest common factor will be the largest of these.</p>\n<p></p>\n<p>For $\\var{fourfac}$ and $\\var{sixfac}$, the highest common factor&nbsp;is $\\var{hc}$.</p>\n<h4>c)</h4>\n<p>Dividing both the numerator and denominator by the highest common factor gives:</p>\n<p>\\[ \\frac{\\var{sixfac}}{\\var{fourfac}} =&nbsp;\\frac{\\frac{\\var{sixfac}}{\\var{hc}}}{\\frac{\\var{fourfac}}{\\var{hc}}} =&nbsp;\\frac{\\var{sixfac/hc}}{\\var{fourfac/hc}}\\text{.}\\]</p>\n<p><em></em></p>", "statement": "<p>Simplify $\\var{sixfac}/\\var{fourfac}$ by finding the highest common factor.</p>", "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n", "js": ""}, "variables": {"fourfac": {"templateType": "anything", "description": "", "name": "fourfac", "group": "Ungrouped variables", "definition": "random(27,33,39)"}, "hc": {"templateType": "anything", "description": "", "name": "hc", "group": "Ungrouped variables", "definition": "gcd(sixfac,fourfac)"}, "sixfac": {"templateType": "anything", "description": "", "name": "sixfac", "group": "Ungrouped variables", "definition": "random(12,18)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>Identify the factors of the following numbers in ascending order.</p>\n<p><em>i) &nbsp; &nbsp;&nbsp;</em>Factors of $\\var{fourfac}$: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;$1$, [[4]],&nbsp;[[5]], $\\var{fourfac}$</p>\n<p></p>\n<p><em>ii) &nbsp; &nbsp;&nbsp;</em>Factors of $\\var{sixfac}$: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[0]], $2$,&nbsp;[[1]],&nbsp;[[2]], $\\var{sixfac/2}$,&nbsp;[[3]]</p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "1", "allowFractions": false, "minValue": "1", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "3", "allowFractions": false, "minValue": "3", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "{sixfac/3}", "allowFractions": false, "minValue": "{sixfac/3}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "{sixfac}", "allowFractions": false, "minValue": "{sixfac}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "3", "allowFractions": false, "minValue": "3", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "0.5", "maxValue": "{fourfac/3}", "allowFractions": false, "minValue": "{fourfac/3}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}], "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>What is the heighest common factor of $\\var{fourfac}$ and $\\var{sixfac}$?</p>\n<p>The heighest common factor is [[0]]</p>", "stepsPenalty": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": "1", "maxValue": "hc", "allowFractions": false, "minValue": "hc", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>If the same number appears in a list of factors for two numbers, it is a common factor. The largest of these common factors is the highest common factor.</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "information", "marks": 0, "scripts": {}}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>Use the result above to&nbsp;reduce the following fraction to its simplest form.</p>\n<p>$\\displaystyle \\frac{\\var{sixfac}}{\\var{fourfac}} = $ <fraction> <numerator>[[0]]</numerator> <denominator>[[1]]</denominator> </fraction></p>", "stepsPenalty": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": 1, "maxValue": "sixfac/hc", "allowFractions": false, "minValue": "sixfac/hc", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}, {"variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "type": "numberentry", "marks": 1, "maxValue": "fourfac/hc", "allowFractions": false, "minValue": "fourfac/hc", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "mustBeReducedPC": 0}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>To simplify the fraction, divide both the numerator and denominator by the highest common factor.</p>", "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "information", "marks": 0, "scripts": {}}], "showCorrectAnswer": true}], "tags": ["composite numbers", "factors", "Factors", "highest common factors", "prime numbers", "taxonomy"], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}]}]}], "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}]}