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1.为什么不把“1”也归入质数一类? 全体自然数可以分成三类:一类是质数;另一类是合数;“1”既不算质数,也不算合数,单独算一类。质数只能被1和它本身整除,而合数还能被其它数整除,所以把质数和合数分成两类的理由很充足。“1”也能被1和它本身整除,如果把“1”也算作质数,那么把自然数分成质数和合数两类,不是更好吗? 要回答这个问题,让我们先从一个小例子谈起。比如说,2618能够被哪些数整除,也就是说,2618的因数有哪一些。我们知道,可以把合数分解质因数,而且分解质因数的结果只有一种。2618分解质因数的结果是2618=2×7×11×17。 现在我们再来看看,如果“1”也算作质数,那么把一个合数分解成质因数的时候,它的答案就不止一个了。
1. Why do not “1” also belong to the prime class? All natural numbers can be divided into three categories: one is the prime number; the other is the composite number; “1” is neither prime nor complex, alone Count a class. The prime number can only be divisible by 1 and itself, and the composite number can also be divisible by other numbers, so the rationale for dividing the prime numbers and the composite numbers into two categories is sufficient. “1” is also divisible by 1 and itself. If “1” is also counted as a prime number, is it not better to divide natural numbers into primes and combined numbers? To answer this question, let us start with a small example Start. For example, 2618 can be divided by what number, that is, what are the factors of 2618. We know that it is possible to decompose the composite number by the factor, and there is only one solution to the qualitative factor. The result of the 2618 digestibility factor is 2618 = 2 × 7 × 11 × 17. Now let us see if “1” is also considered a prime number, then there is more than one answer to a composite number broken down into primes.