Wednesday, 14 October 2015
HCF AND LCM WITH BRACH METHOD CALCULATOR CODE
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COPY AND PASTE BELOW CODE IN POST HTML SECTION
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<html ng-app>
<head>
<h1>HIGHEST COMMON FACTOR AND LOWEST COMMON MULTIPLE</h1>
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<script>
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</style>
<style type="text/css">
.tight.list-inline li {
padding-left: 2px;
padding-right: 2px;
}
.tight.list-inline li:first-child {
padding-left: 5px;
}
.tight input, .input-width{
width: 11em;
}
span.w {
display: inline-block;
width: 56px;
text-align: center;
}
span.wh {
display: inline-block;
width: 28px;
text-align: center;
}
.tree li{
margin-top: 7px;
}
.tree li:first-child{
margin-left: 33px;
}
.tree li div{
display: inline-block;
}
.my-inline {
display: inline-block;
}
ul ul.list-inline {
display: inline-block;
}
small input[type=checkbox] {
vertical-align: top;
}
.indent {
margin-left: 2em;
}
.label.large {
font-size: 85%;
}
table.tight td{
padding-right: 4px;
padding-bottom: 2px;
}
table.primes td {
padding-right: 10px;
padding-bottom: 10px;
}
.nowrap {
white-space: nowrap;
}
.label.label-empty {
color: #000;
}
.unselectable {
-webkit-touch-callout: none;
-webkit-user-select: none;
-khtml-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
</style>
</head>
<body ng-controller="Ctrl">
<br>
<div class="container">
<div class="alert alert-danger" ng-show="error">
Oops, a mistake was made calculating the HCF and LCM!
</div>
<h4>Divided into Prime Factors</h4>
<table class="tight">
<tr ng-repeat="num in nums">
<td>
<form name="form" ng-submit="nums.push({n: 2});">
<input type="number" placeholder="Enter number" min="2" max="500000" class="form-control" required
ng-model="num.n" name="num" ng-focus="num.focus = true;" ng-blur="num.focus = false;">
</form>
</td>
<td> = </td>
<td>
<span ng-hide="form.num.$valid" class="text-danger">Number should be between 2 and 500000</span>
<span ng-repeat="f in num.factors track by $index">
<span>{{f.factor}}</span>
<span ng-hide="$last"> × </span>
</span>
</td>
<td> = </td>
<td>
<span ng-repeat="(f, e) in num.expFactors">
<b>{{f}}<sup>{{e.exp}}</sup></b>
<span ng-hide="$last"> × </span>
</span>
</td>
</tr>
</table>
<button class="btn btn-default input-width" ng-click="nums.push({n: 2});">Add another</button>
<hr>
<h4>Highest Common Factor</h4>
<div class="indent">
<ul class="list-inline tight my-inline">
<li><b> HCF ({{ _.map(nums, 'n').join(',') }}) </b></li>
<li> = </li>
<li ng-repeat="f in gcdFactors track by $index">
<span class="label label-info">{{f}}</span>
<span ng-hide="$last"> × </span>
</li>
<li> = </li>
<li ng-repeat="(f, exp) in gcdExpFactors">
<b class="label label-success large">{{f}}<sup>{{exp}}</sup></b>
<span ng-hide="$last"> × </span>
</li>
<li> = </li>
<li>{{gcd}}</li>
</ul>
<br><br>
<table class="tight">
<tr ng-repeat="num in nums">
<td> {{num.n}} </td>
<td> = </td>
<td>
<span ng-repeat="f in num.factors track by $index">
<span ng-class="{'label label-info': f.gcd}">{{f.factor}}</span>
<span ng-hide="$last"> × </span>
</span>
</td>
<td> = </td>
<td>
<span ng-repeat="(f, e) in num.expFactors">
<b ng-class="{'label label-success large': e.gcd}">{{f}}<sup>{{e.exp}}</sup></b>
<span ng-hide="$last"> × </span>
</span>
</td>
</tr>
</table>
<br>
<p>Look at the prime factors in index form. See which factors are common to each number (appear in all of the rows) and take the ones with the smallest power and multiply them all together</p>
</div>
<hr>
<h4>Lowest Common Multiple</h4>
<div class="indent">
<ul class="list-inline tight my-inline">
<li><b> LCM ({{ _.map(nums, 'n').join(',') }}) </b></li>
<li> = </li>
<li ng-repeat="f in lcmFactors track by $index">
<span class="label label-info">{{f}}</span>
<span ng-hide="$last"> × </span>
</li>
<li> = </li>
<li ng-repeat="(f, exp) in lcmExpFactors">
<b class="label label-success large">{{f}}<sup>{{exp}}</sup></b>
<span ng-hide="$last"> × </span>
</li>
<li> = </li>
<li>{{lcm}}</li>
</ul>
<br><br>
<table class="tight">
<tr ng-repeat="num in nums">
<td> {{num.n}} </td>
<td> = </td>
<td>
<span ng-repeat="f in num.factors track by $index">
<span ng-class="{'label label-info': f.lcm}">{{f.factor}}</span>
<span ng-hide="$last"> × </span>
</span>
</td>
<td> = </td>
<td>
<span ng-repeat="(f, e) in num.expFactors">
<b ng-class="{'label label-success large': e.lcm}">{{f}}<sup>{{e.exp}}</sup></b>
<span ng-hide="$last"> × </span>
</span>
</td>
</tr>
</table>
<br>
<p>Look at the prime factors in index form. Take the ones with the largest power and multiply them all together. Note that these do not have to be common this time.</p><br><br>
</div>
</div>
<script>
'use strict';
function Ctrl($scope) {
function generatePrimes(max) {
// Eratosthenes algorithm to find all primes under max
var array = _.range(max);
for (var i = 2; i <= Math.sqrt(max); i++) {
if (array[i]) {
for (var j = i*i; j < max; j += i) {
array[j] = false;
}
}
}
return _.compact(_.tail(array, 2));
}
$scope.primes = generatePrimes(500000);
$scope._ = _;
// $scope.nums = [{n: 27}, {n: 36}, {n: 45}];
$scope.nums = [{n: 3*3*3*3 * 2*2}, {n: 3*3*3*3 * 2}, {n: 3*3*3 * 2*2}, {}, {}, {}];
function primeFactors(n) {
function isFactor(prime) {
return n%prime === 0;
}
var factors = [];
while (n > 1) {
var factor = _.find($scope.primes, isFactor);
n = n / factor;
factors.push({factor: factor, gcd: false});
}
return factors;
}
function calcGCDab(a, b) {
if (!b) return a;
return calcGCDab(b, a%b);
}
function calcGCD(arr) {
return _.reduce(_.compact(arr), calcGCDab);
}
function calcLCMab(a, b) {
return a*b / calcGCDab(a,b);
}
function calcLCM(arr) {
return _.reduce(_.compact(arr), calcLCMab);
}
$scope.$watchCollection(function () {
return _.map($scope.nums, function (num){ return num.n + num.focus; });
}, function () {
$scope.nums = _.filter($scope.nums, function (num) {
return num.n || num.focus;
});
_.each($scope.nums, function (num) {
num.factors = primeFactors(num.n);
num.expFactors = _.mapValues(_.countBy(num.factors, 'factor'), function (exp) {
return {exp: exp, gcd: false, lcm: false};
});
});
var goodnums = _.filter($scope.nums, 'n');
var allFactors = _.map(goodnums, 'expFactors');
// gcd factors
var gcdFactorsOnly = _.intersection.apply(_, _.map(allFactors, _.keys));
$scope.gcdExpFactors = _.mapValues(_.indexBy(gcdFactorsOnly), function (f) {
return _.min(_.map(_.map(allFactors, f), 'exp'));
});
if (_.isEmpty($scope.gcdExpFactors)) $scope.gcdExpFactors = {1: 1};
$scope.gcdFactors = _.flatten(_.map($scope.gcdExpFactors, function (exp, factor) {
return _.map(_.range(exp), function () { return factor; });
}));
$scope.gcd = _.reduce($scope.gcdFactors, function (acc, f) { return acc*f; }, 1);
$scope.error = calcGCD(_.map(goodnums, 'n')) != $scope.gcd;
var expGCD = angular.copy($scope.gcdExpFactors);
_.each(goodnums, function (num) {
expGCD = angular.copy($scope.gcdExpFactors);
_.each(num.factors, function (f) {
f.gcd = expGCD[f.factor] > 0;
expGCD[f.factor]--;
});
});
expGCD = angular.copy($scope.gcdExpFactors);
_.eachRight(goodnums, function (num) {
_.each(num.expFactors, function (e, f) {
if (expGCD[f] && expGCD[f] == e.exp) {
e.gcd = true;
delete expGCD[f];
}
});
});
// lcm factors
var lcmFactorsOnly = _.union.apply(_, _.map(allFactors, _.keys));
$scope.lcmExpFactors = _.mapValues(_.indexBy(lcmFactorsOnly), function (f) {
return _.max(_.map(_.compact(_.map(allFactors, f)), 'exp'));
});
$scope.lcmFactors = _.flatten(_.map($scope.lcmExpFactors, function (exp, factor) {
return _.map(_.range(exp), function () { return factor; });
}));
$scope.lcm = _.reduce($scope.lcmFactors, function (acc, f) { return acc*f; }, 1);
$scope.error = calcLCM(_.map(goodnums, 'n')) != $scope.lcm;
var expLCMfloatingMax = _.mapValues($scope.lcmExpFactors, function () { return 0; });
_.each(goodnums, function (num) {
var addableExp = _.mapValues(num.expFactors, function (e, f) {
var ret = e.exp - expLCMfloatingMax[f];
if (ret > 0) expLCMfloatingMax[f] = e.exp;
return ret;
});
_.eachRight(num.factors, function (f) {
f.lcm = addableExp[f.factor] > 0;
addableExp[f.factor]--;
});
});
var expLCM = angular.copy($scope.lcmExpFactors);
_.eachRight(goodnums, function (num) {
_.each(num.expFactors, function (e, f) {
if (expLCM[f] && expLCM[f] == e.exp) {
e.lcm = true;
delete expLCM[f];
}
});
});
});
}
</script>
</body>
</html>
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