Algorithm analysis Exercises (1)

12.1

1. The qualitative factor is in number theory, the mass factor of a positive integer refers to the integer of prime numbers that can be divisible by the numbers.

Two positive integers without a common mass factor are called coprime. The factorization of positive integers gives a series of qualitative factors, after all the mass factors are multiplied. Qualitative factors such as repetition will be expressed as an exponent. According to fundamental theorem of arithmetic, any positive integer has a unique factorization of the mass factor.

There are 25 prime numbers (primes) within 1-100, and 1 are neither prime nor composite. 0 and 1 are neither prime numbers nor composite. First: The division of numbers is divided into the categories of non-0 natural numbers, so prime numbers and composite certainly do not include 0. Take a look at the natural number "1". Prime numbers are natural numbers that contain 1 and 2 factors of itself, while the natural number "1" is only 1 of these 1 factors, so the natural number "1" does not meet the requirements of prime numbers, then "1" is not prime. Composite refers to the number of other factors besides 1 and its own 2 factors. That is to say, Composite has at least 3 factors, it is clear that the natural number "1" does not conform to the definition of composite, so 1 is neither prime nor composite.

Up to approximate questions turn from: http://blog.csdn.net/net_assassin/article/details/8960725

Algorithm analysis Exercises (1)