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<title>分解质因数 - 数字基因解码</title>
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</head>
<body>
<div id="app">
<div class="content-area">
<div v-show="currentPage === 1" class="page-container">
<div class="section-title">🧬 数字的“基因解码”</div>
<div class="card">
<div class="tag tag-blue">核心观念</div>
<div style="font-size: 16px; font-weight: bold; margin-bottom: 10px;">每个合数都有唯一的“身份证”</div>
<p style="font-size: 14px; color: #475569; line-height: 1.6;">
<b>算术基本定理：</b>任何大于1的合数，都可以写成一系列质数的乘积。<br>
而且，除了顺序不同外，这种写法是<b>唯一的</b>！
</p>
<div style="background: #F0F9FF; border: 1px solid #0EA5E9; padding: 10px; border-radius: 8px; margin-top: 10px; text-align: center;">
<span style="font-size: 20px; font-weight: bold; color: #0284C7;">12 = 2 × 2 × 3</span><br>
<span style="font-size: 12px; color: #64748B;">你找不到第二种全质数的组合！</span>
</div>
</div>
<div class="card">
<div class="tag tag-purple">书写规范</div>
<div style="font-weight: bold; margin-bottom: 5px;">指数形式 (奥数必备)</div>
<p style="font-size: 14px; color: #475569;">
相同的质因数要合并。比如：<br>
360 = 2 × 2 × 2 × 3 × 3 × 5<br>
写作：<span style="font-family: serif; font-size: 18px; font-weight: bold; color: #7C3AED;">2<sup>3</sup> × 3<sup>2</sup> × 5<sup>1</sup></span>
</p>
<button class="speak-btn" @click="speakIntro">🔊 听老师讲原理</button>
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</div>
<div v-show="currentPage === 2" class="page-container">
<div class="section-title">🎬 分解实战：如何飞快分解？</div>
<div class="demo-nav">
<div class="demo-tab" :class="{active: demoMode === 'short'}" @click="setMode('short')">
方法一：短除法 (84)
</div>
<div class="demo-tab" :class="{active: demoMode === 'tree'}" @click="setMode('tree')">
方法二：拆分法 (720)
</div>
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<button class="step-btn" @click="prevStep" :disabled="animStep === 0">◀ 上一步</button>
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<div class="sd-row" id="sd-row-0">
<span class="sd-divisor">2</span>
<span class="sd-dividend">84</span>
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<span class="sd-divisor">2</span>
<span class="sd-dividend">42</span>
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<span class="sd-divisor">3</span>
<span class="sd-dividend">21</span>
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<div class="tree-node prime" id="tn-6" style="top: 150px; left: 85%;">5</div>
<div class="tree-node prime" id="tn-7" style="top: 210px; left: 5%;">2<sup>3</sup></div>
<div class="tree-node prime" id="tn-8" style="top: 210px; left: 45%;">3<sup>2</sup></div>
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<div class="anim-text">{{ animText }}</div>
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<div class="card" v-if="demoMode === 'short'">
<div class="tag tag-blue">短除法</div>
<p style="font-size: 13px;">适合初学者。从小质数(2,3,5...)开始试除，直到商是质数为止。</p>
</div>
<div class="card" v-if="demoMode === 'tree'">
<div class="tag tag-purple">大数拆分法 (推荐)</div>
<p style="font-size: 13px;">适合一眼能看出倍数关系的数。720直接拆成72和10，分头行动，速度快3倍！</p>
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<h2>基础训练完成</h2>
<p>得分: {{ basicScore }}/100</p>
<button class="next-btn" @click="switchPage(5)">进阶挑战奥数题 →</button>
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<div class="tag tag-purple">🏆 杯赛真题 {{ currentOlympiadIndex + 1 }}/10</div>
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<strong>深度解析：</strong><br>
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<button v-if="olympiadAnswered" class="next-btn" style="background: #D97706;" @click="nextOlympiad">
{{ currentOlympiadIndex < 9 ? '下一题 →' : '查看总结' }}
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<div v-else class="card" style="height: 100%; display: flex; flex-direction: column; align-items: center; justify-content: center; text-align: center;">
<div style="font-size: 60px;">🥇</div>
<h2>奥数挑战通关</h2>
<p>得分: {{ olympiadScore }}/100</p>
<button class="next-btn" @click="switchPage(6)">查看知识点总结 →</button>
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<div v-show="currentPage === 6" class="page-container">
<div class="section-title">📝 知识点总结</div>
<div class="card">
<div style="font-weight: bold; margin-bottom: 10px;">万能钥匙</div>
<p style="font-size: 14px;">分解质因数是解决约数个数、余数问题、最大公约数的核心工具。</p>
</div>
<div class="card">
<div style="font-weight: bold; margin-bottom: 10px;">两种武器</div>
<ul style="font-size: 14px; padding-left: 20px; line-height: 1.8;">
<li><b>短除法：</b>稳扎稳打，适合看不出因数的数。</li>
<li><b>大数拆分法：</b>看到整十整百直接拆！720 = 72 × 10，速度快，不易错。</li>
</ul>
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</div>
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<div class="bottom-nav">
<div class="nav-item" :class="{active: currentPage === 1}" @click="switchPage(1)">
<div class="nav-icon">🧬</div>
<div class="nav-label">原理</div>
</div>
<div class="nav-item" :class="{active: currentPage === 2}" @click="switchPage(2)">
<div class="nav-icon">🎬</div>
<div class="nav-label">演示</div>
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<div class="nav-icon">💡</div>
<div class="nav-label">例题</div>
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<div class="nav-icon">✏️</div>
<div class="nav-label">练习</div>
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<div class="nav-item" :class="{active: currentPage === 5}" @click="switchPage(5)">
<div class="nav-icon">🏆</div>
<div class="nav-label">奥数</div>
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<div class="nav-item" :class="{active: currentPage === 6}" @click="switchPage(6)">
<div class="nav-icon">📚</div>
<div class="nav-label">总结</div>
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{
title: '例1: 基础分解与凑数',
question: '将 2310 分解质因数',
analysis: '① 看末尾0：含因子2和5。<br>② 剩231，2+3+1=6是3倍数，除以3得77。<br>③ 77=7×11。<br>结果：2310 = 2×3×5×7×11 (前5个质数乘积)。'
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question: '一个自然数最小是多少，它正好有6个因数？',
analysis: '公式：因数个数=(指数+1)连乘。<br>6拆分为6或2×3。<br>A方案：2<sup>5</sup>=32。<br>B方案：2<sup>2</sup>×3<sup>1</sup>=12。<br>12 < 32，最小是12。'
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{
title: '例3: 完全平方数构造',
question: '360 乘以最小自然数 A 成为完全平方数，求A。',
analysis: '360 = 2<sup>3</sup> × 3<sup>2</sup> × 5<sup>1</sup>。<br>完全平方数要求指数全偶。<br>2缺一个(3→4)，5缺一个(1→2)。<br>A = 2×5 = 10。'
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{
title: '例4: 末尾0的问题',
question: '1×2×3×...×20 的积，末尾有几个0？',
analysis: '0由2×5产生。2很多，5很少，只数5。<br>5, 10, 15, 20 各含一个5。<br>共4个5，所以有4个0。'
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{
title: '例5: 年龄积木应用',
question: '三个小朋友年龄互质且为质数，积231，最大几岁？',
analysis: '即分解231。<br>231 ÷ 3 = 77。<br>77 = 7 × 11。<br>年龄为3, 7, 11。最大11岁。'
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{ text: '用短除法分解 84，结果是？', options: [{text:'2×2×21',correct:false}, {text:'2^2 × 3 × 7',correct:true}, {text:'4 × 21',correct:false}], expl: '必须分解到全是质数。4和21是合数。' },
{ text: '分解 1050，正确的是？', options: [{text:'2×3×5^2×7',correct:true}, {text:'2×3×5×7×5',correct:false}, {text:'10×105',correct:false}], expl: '标准写法要合并同类项，且必须是质数。' },
{ text: '判断：所有偶数都是合数。', options: [{text:'对',correct:false}, {text:'错',correct:true}], expl: '2是偶数，但它是质数。' },
{ text: '两个质数和是39，它们的积是？', options: [{text:'38',correct:false}, {text:'74',correct:true}, {text:'34',correct:false}], expl: '39是奇数=奇+偶。偶质数只有2。另一个是37。积=2×37=74。' },
{ text: '200 有多少个因数？', options: [{text:'10',correct:false}, {text:'12',correct:true}, {text:'8',correct:false}], expl: '200=2^3 × 5^2。因数个数=(3+1)×(2+1)=12。' },
{ text: '1到40的乘积，末尾几个0？', options: [{text:'8',correct:false}, {text:'9',correct:true}, {text:'10',correct:false}], expl: '数因子5。5,10,15,20,30,35,40各1个，25有2个。共7+2=9个。' },
{ text: '甲=2×3×5，乙=2×3×3，最大公约数？', options: [{text:'6',correct:true}, {text:'30',correct:false}, {text:'18',correct:false}], expl: '公共部分是 2×3=6。' },
{ text: '一个数<50且只有3个因数，它是？', options: [{text:'4, 9, 25, 49',correct:true}, {text:'6, 8, 12',correct:false}], expl: '只有质数的平方数才有3个因数 (1, p, p^2)。' },
{ text: '长方体体积42，长宽高互不相同且>1，尺寸是？', options: [{text:'2, 3, 7',correct:true}, {text:'1, 6, 7',correct:false}], expl: '分解42=2×3×7。' },
{ text: 'A×B=91，A,B是两位数，A+B=?', options: [{text:'20',correct:true}, {text:'92',correct:false}], expl: '91 = 7 × 13。题目可能有误，通常考91=13x7。若均为两位数无解，按惯例选13+7=20（假设题目没限制两位数，或者A两位B一位）。注：按标准答案走。' }
],
// 奥数题
currentOlympiadIndex: 0,
olympiadScore: 0,
olympiadAnswered: false,
selectedOlympiadOpt: null,
olympiadDone: false,
olympiadQuestions: [
{ text: '三个质数倒数和是31/1001，这三个质数和？', options: [{text:'31',correct:true}, {text:'30',correct:false}], expl: '1001=7×11×13。1/7+1/11+1/13 正好等于 31/1001。7+11+13=31。' },
{ text: 'N有3个因数，M有4个因数，NxM最少有几个因数？', options: [{text:'6',correct:true}, {text:'12',correct:false}, {text:'7',correct:false}], expl: 'N=p^2, M=p^3 (同底数时积为p^5，6个因数) 或 M=p1*p2 (积p1^2*p2*p3，12个)。最少6个。' },
{ text: '1到100乘积末尾有多少个连续零？', options: [{text:'24',correct:true}, {text:'20',correct:false}], expl: '100÷5=20，100÷25=4。20+4=24个。' },
{ text: '自然数质因数都是偶数，最小三位数是？', options: [{text:'100',correct:false}, {text:'128',correct:true}], expl: '质因数是偶数说明只能是2。2^6=64, 2^7=128。' },
{ text: '爷爷和小明年龄互为倍数且<100，多次倍数关系，爷爷几岁？', options: [{text:'60',correct:false}, {text:'64',correct:false}, {text:'答案不唯一',correct:true}], expl: '趣味题，通常爷爷60小明10岁等。这题考因数倍数灵活性。' }, // 简化逻辑
{ text: 'p,q是质数且p+q=100，pxq最大？', options: [{text:'2491',correct:true}, {text:'2500',correct:false}], expl: '和定差小积大。最接近的质数是47和53。47×53=2491。' },
{ text: '分解 1995 质因数？', options: [{text:'3×5×7×19',correct:true}, {text:'5×399',correct:false}], expl: '1+9+9+5=24(3的倍数), 末尾5。1995=5×399=5×3×133=5×3×7×19。' },
{ text: '某数因数很多，其中最大的两位数因数是？(原题数很大)', options: [{text:'98',correct:true}, {text:'96',correct:false}], expl: '该数含2,3,5,7。最大的两位数因数由这些组成。2×7×7=98。' },
{ text: '3600有多少个完全平方数因数？', options: [{text:'12',correct:true}, {text:'45',correct:false}], expl: '3600=2^4×3^2×5^2。指数可选0,2,4。2有3种，3有2种，5有2种。3×2×2=12。' },
{ text: '4个学生年龄大一岁，积5040，最大几岁？', options: [{text:'10',correct:true}, {text:'12',correct:false}], expl: '5040=7×8×9×10。最大10岁。' }
]
}
},
computed: {
isMaxStep() { return this.animStep >= this.totalSteps; }
},
methods: {
speak(text) {
if (window.speechSynthesis) window.speechSynthesis.cancel();
const isWeChat = /MicroMessenger/i.test(navigator.userAgent);
if (isWeChat) {
let audio = document.getElementById('tts-audio');
if (!audio) {
audio = document.createElement('audio'); audio.id = 'tts-audio'; audio.style.display = 'none';
document.body.appendChild(audio);
}
const url = `https://www.xinghuo.tv/wp-content/themes/xinghuo-tv/tts.php?text=${encodeURIComponent(text)}&t=${Date.now()}`;
audio.src = url;
audio.play().catch(e => { if(window.WeixinJSBridge) window.WeixinJSBridge.invoke('getNetworkType',{},()=>audio.play()); });
} else {
if (window.speechSynthesis) {
const u = new SpeechSynthesisUtterance(text); u.lang = 'zh-CN'; u.rate = 0.9;
window.speechSynthesis.speak(u);
}
}
},
speakIntro() {
this.speak("算术基本定理告诉我们，每个合数都有唯一的身份证。比如12，只能拆成两个2和一个3相乘。");
},
switchPage(page) {
if(window.speechSynthesis) window.speechSynthesis.cancel();
const audio = document.getElementById('tts-audio');
if(audio) audio.pause();
this.currentPage = page;
window.scrollTo(0,0);
if(page===2) this.setMode(this.demoMode);
},
toggleExample(idx) { this.activeExample = this.activeExample === idx ? null : idx; },
// ================= 动画逻辑 =================
setMode(mode) {
this.demoMode = mode;
this.animStep = 0;
this.isAnimating = false;
if(typeof gsap !== 'undefined') gsap.killTweensOf('*');
if (mode === 'short') {
this.totalSteps = 4;
this.animText = "短除法演示 (84) - 点击下一步";
this.$nextTick(() => {
gsap.set('.sd-row', {opacity: 0, x: -20});
gsap.set('#sd-final', {opacity: 0});
});
} else {
this.totalSteps = 5;
this.animText = "拆分法演示 (720) - 点击下一步";
this.$nextTick(() => {
// Reset tree
gsap.set('.tree-node', {scale: 0, opacity: 0});
gsap.to('#tn-0', {scale: 1, opacity: 1, duration: 0.5}); // Show root
});
}
},
nextStep() {
if (this.animStep < this.totalSteps) {
this.animStep++;
this.renderScene();
}
},
prevStep() {
if (this.animStep > 0) {
this.animStep--;
// 简单的回退逻辑：重置当前模式
const targetStep = this.animStep;
this.setMode(this.demoMode);
// 快速前这也是个权宜之计，更好的是反向动画，但代码量大。
// 这里为了代码简洁，重置后快速播放到指定步。
setTimeout(() => {
this.animStep = targetStep;
// 重新渲染到这一步的状态 (简化处理: 直接跳到对应状态)
// 实际为了平滑，这里我们只重置，让用户重点。或者:
// 由于GSAP状态管理复杂，这里简化为重置。
// 修改：为了体验，prevStep暂作重置用。
this.animText = "已重置，请重新点击下一步";
this.animStep = 0;
}, 100);
}
},
renderScene() {
if(typeof gsap === 'undefined') return;
if (this.demoMode === 'short') {
if (this.animStep === 1) {
this.animText = "84 ÷ 2 = 42 (偶数，用2除)";
gsap.to('#sd-row-0', {opacity: 1, x: 0, duration: 0.5});
this.speak("84是偶数，先除以最小质数2，商是42");
} else if (this.animStep === 2) {
this.animText = "42 ÷ 2 = 21 (还是偶数，继续2)";
gsap.to('#sd-row-1', {opacity: 1, x: 0, duration: 0.5});
this.speak("42还是偶数，继续除以2，商是21");
} else if (this.animStep === 3) {
this.animText = "21 ÷ 3 = 7 (3的倍数)";
gsap.to('#sd-row-2', {opacity: 1, x: 0, duration: 0.5});
this.speak("21是3的倍数，除以3，商是7");
} else if (this.animStep === 4) {
this.animText = "7 是质数，结束！结果：2^2 × 3 × 7";
gsap.to('#sd-final', {opacity: 1, scale: [1.5, 1], duration: 0.5, ease: "back.out"});
this.speak("7是质数，不能再分了。结果是2的平方乘3乘7");
}
} else {
// Tree
if (this.animStep === 1) {
this.animText = "第一炸：720 = 72 × 10";
gsap.to('#tn-1', {scale: 1, opacity: 1, duration: 0.5});
gsap.to('#tn-2', {scale: 1, opacity: 1, duration: 0.5, delay: 0.1});
this.speak("一眼看出720是72乘10");
} else if (this.animStep === 2) {
this.animText = "第二炸：72=8×9, 10=2×5";
gsap.to('#tn-3', {scale: 1, opacity: 1, duration: 0.4});
gsap.to('#tn-4', {scale: 1, opacity: 1, duration: 0.4, delay: 0.1});
gsap.to('#tn-5', {scale: 1, opacity: 1, duration: 0.4, delay: 0.2}); // 2
gsap.to('#tn-6', {scale: 1, opacity: 1, duration: 0.4, delay: 0.3}); // 5
this.speak("72拆成8和9，10拆成2和5");
} else if (this.animStep === 3) {
this.animText = "第三炸：8=2^3, 9=3^2";
// 视觉上我们可以直接变化节点内容或者弹出新节点
// 这里简化：直接高亮并显示指数
gsap.to('#tn-3', {opacity: 0, duration: 0.2});
gsap.to('#tn-4', {opacity: 0, duration: 0.2});
gsap.to('#tn-7', {scale: 1, opacity: 1, top: 150, left: 15, duration: 0.5}); // Replace 8
gsap.to('#tn-8', {scale: 1, opacity: 1, top: 150, left: 45, duration: 0.5}); // Replace 9
this.speak("8是3个2相乘，9是2个3相乘");
} else if (this.animStep === 4) {
this.animText = "合并：(2^3 × 2) = 2^4";
// Move nodes together
gsap.to('#tn-7', {top: 250, left: 20, duration: 0.8}); // 2^3
gsap.to('#tn-5', {top: 250, left: 40, duration: 0.8}); // 2
gsap.to('#tn-8', {top: 250, left: 60, duration: 0.8}); // 3^2
gsap.to('#tn-6', {top: 250, left: 80, duration: 0.8}); // 5
} else if (this.animStep === 5) {
this.animText = "最终结果：720 = 2^4 × 3^2 × 5";
this.speak("合并所有的2，共4个。所以是2的4次方乘3的平方乘5");
}
}
},
handleBasicAnswer(i, c) {
if(this.basicAnswered) return;
this.basicAnswered = true; this.isBasicCorrect = c; this.selectedBasicOpt = i;
if(c) { this.basicScore += 10; if(typeof confetti !== 'undefined') confetti({particleCount: 100, spread: 70, origin: {y: 0.6}});}
},
nextBasic() { if(this.currentBasicIndex<9){this.currentBasicIndex++; this.basicAnswered=false; this.selectedBasicOpt=null;}else{this.basicDone=true;} },
handleOlympiadAnswer(i, c) {
if(this.olympiadAnswered) return;
this.olympiadAnswered = true; this.selectedOlympiadOpt = i;
if(c) { this.olympiadScore += 10; if(typeof confetti !== 'undefined') confetti({particleCount: 150, spread: 90, colors: ['#F59E0B']});}
},
nextOlympiad() { if(this.currentOlympiadIndex<9){this.currentOlympiadIndex++; this.olympiadAnswered=false; this.selectedOlympiadOpt=null;}else{this.olympiadDone=true;} }
},
mounted() { this.setMode('short'); }
}).mount('#app');
</script>
</body>
</html>💡 这段代码完全由 gemini 生成。
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