📚 The Number 240: Prime Factorisation, HCF, LCM and Beyond | 数字240：质因数分解、最大公因数、最小公倍数及其扩展
In IGCSE Mathematics, the number 240 appears in many exercises on prime factorisation, highest common factor (HCF) and lowest common multiple (LCM). Understanding the properties of 240 helps build strong number skills, which are essential for algebra, fractions and problem solving. This article explores 240 from different angles, providing clear explanations and examples in both English and Chinese.
在IGCSE数学中，数字240经常出现在质因数分解、最大公因数（HCF）和最小公倍数（LCM）的练习中。理解240的性质有助于打下坚实的数感基础，这对代数、分数和解决问题都至关重要。本文从不同角度探索240，并提供清晰的双语解释和示例。
1. Introduction: Why Study 240? | 引言：为什么要研究240？
The number 240 is highly composite, meaning it has many factors. It appears in everyday life – 240 minutes equal 4 hours, 240 pence is £2.40, and a circle split into 240 equal parts gives sectors of 1.5 degrees each. In IGCSE, working with a rich number like 240 allows you to practise key syllabus points such as writing a number as a product of prime factors, using index notation, and finding HCF and LCM by prime factorisation.
数字240是一个高合成数，意味着它有许多因数。它在日常生活中经常出现——240分钟等于4小时，240便士是2.40英镑，一个圆如果分成240等份，每个扇形的角度为1.5度。在IGCSE中，使用像240这样内涵丰富的数字可以让你练习大纲中的关键内容，例如将数字写成质因数的乘积、使用指数记号以及通过质因数分解求最大公因数和最小公倍数。
This article will take you step by step through the prime factorisation of 240, listing all its factors, calculating the number of factors systematically, and applying HCF and LCM to solve problems involving 240. Real-world contexts connect the mathematics to time, money and geometry.
本文将一步步引导你完成240的质因数分解，列出它的所有因数，系统地计算因数个数，并应用HCF和LCM解决与240有关的问题。实际背景将数学与时间、货币和几何联系起来。
2. Prime Factorisation of 240 | 240的质因数分解
Prime factorisation means breaking down a number into a product of prime numbers. Let' t prime, 3: 15 ÷ 3 = 5. Finally, 5 is prime. So the prime factors are 2, 2, 2, 2, 3 and 5.
质因数分解意味着将一个数字拆分成质数的乘积。我们从240开始。寻找能整除240的最小质数。由于240是偶数，我们除以2：240 ÷ 2 = 120。继续：120 ÷ 2 = 60，60 ÷ 2 = 30，30 ÷ 2 = 15。现在15不能被2整除，因此我们使用下一个质数3：15 ÷ 3 = 5。最后，5是质数。因此质因数为2, 2, 2, 2, 3和5。
sing index notation is essential in IGCSE when answering questions on prime factorisation.
因此，240可以表示为：240 = 2 × 2 × 2 × 2 × 3 × 5。用指数形式表示为 2⁴ × 3 × 5。在IGCSE回答质因数分解问题时，使用指数记号是必需的。
3. Factor Tree Method | 因子树法
A factor tree is a visual method to find prime factors. Start with 240 and split it into any two factors, e.g. 10 and 24. Then break 10 into 2 and 5 (both prime), and break 24 into 2 and 12. Continue breaking 12 into 2 and 6, and 6 into 2 and 3. The prime leaves are 2, 2, 2, 2, 3 and 5 – the same result. Factor trees help students see the multiplication structure and are often drawn in IGCSE exams.
因子树是一种寻找质因数的可视化方法。从240开始，将它拆分成任意两个因数，例如10和24。然后将10拆分成2和5（均为质数），将24拆分成2和12。继续将12拆分成2和6，
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图