📚 Prime Numbers and Prime Factorisation | 质数与质因数分解
The number 197 is a prime number. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In this article we will investigate why 197 is prime, how to test primality, and how to use prime factorisation in IGCSE Mathematics.
数字197是一个质数。质数是大于1的正整数，除1和自身外没有其他正因数。在本文中，我们将研究为什么197是质数，如何检验质数，以及如何在IGCSE数学中使用质因数分解。
1. Definition of Prime Numbers | 质数的定义
A prime number has exactly two distinct positive factors: 1 and the number itself.
质数恰好有两个不同的正因数：1和它本身。
A composite number has more than two positive factors.
合数有多于两个的正因数。
The number 1 is neither prime nor composite.
数字1既不是质数也不是合数。
The number 2 is the only even prime number.
数字2是唯一的偶质数。
Since 197 is greater than 1 and its only factors are 1 and 197, it satisfies the definition of a prime number.
由于197大于1，且它的因数只有1和197，因此它满足质数的定义。
2. Why 197 Is a Prime Number | 为什么197是质数
To check if 197 is prime, we test the prime numbers up to the square root of 197.
要检验197是否为质数，我们测试不超过197平方根的质数。
√197 ≈ 14.03
So we only need to check divisibility by 2, 3, 5, 7, 11 and 13.
因此我们只需检查能否被2、3、5、7、11和13整除。
The table below shows the divisions.
下表展示了除法计算结果。
| Divisor | Quotient | Remainder |
| 2 | 98 | 1 |
| 3 | 更多咨询请联系16621398022（同微信）
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