(Find the factors of an integer) Write a program that reads an integer and displays all its smal

(Find the factors of an integer) Write a program that reads...

Key Concepts

Prime Factorization

Prime factorization is the process of breaking down an integer into a product of prime numbers. This concept is based on the Fundamental Theorem of Arithmetic, which guarantees that every integer greater than 1 can be uniquely expressed as a product of primes, regardless of the order. It is a fundamental tool in number theory and is widely used in various areas of mathematics and computer science.

Prime Numbers

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves. They are considered the basic building blocks of all natural numbers because any integer can be decomposed into a product of primes. Understanding prime numbers is crucial for tasks involving factorization, cryptography, and many algorithms that rely on number theory.

Trial Division

Trial division is a basic algorithm for factorizing an integer by systematically testing for divisibility starting from the smallest prime number and moving upward. It involves dividing the integer by each prime candidate and continuing the process recursively with the quotient, ensuring that the complete set of prime factors is obtained. This method is particularly useful for small integers and serves as an introduction to more complex factorization algorithms.

Transcript

00:01 Okay, in this problem, we're looking to build a program that will find the prime factors of any number.

00:09 And i'm going to use two variables.

00:12 I'll call one current factor and start off with two because that's our lowest prime number.

00:18 And i'm going to say answer string and start that off as a blank answer string.

00:27 And then we're going to get a number from the user.

00:33 And i'll ask for input and integer to be factored.

00:47 And that'll get us a number from the user.

00:50 And what we're going to do is whenever we find a prime factor, we're going to divide the number by the prime factor.

00:56 We're going to keep doing that until number becomes one.

01:00 And so i can use a while loop.

01:04 As long as that number is greater than one, i know i still have work to do.

01:10 And so the first thing i'm going to do is going to test to see if the number, whatever number i'm at, is evenly divisible by the current factor.

01:20 So i'm going to use modulo division divided by current factor.

01:29 And if that is exactly equal to 0 ,000, then i know that it evenly divides and i want to do two things when that happens.

01:38 First is i want to update my answer string by adding the current factor to it.

01:48 And so i've got to convert current factor to a string.

01:56 And the second thing i need to do is i need to make my number smaller by dividing it by the current factor.

02:05 And i know that's still going to be an infinite number smaller.

02:07 Integer because i made sure that it divides equally.

02:14 If for some reason i don't find, for some reason that the number isn't equally divisible by current factor, then i need a different current factor.

02:27 So i'm gonna say current factor.

02:31 And all i'm gonna do, i'm not gonna try to keep track of what all the primes are.

02:34 I'm just going to increment this by one...

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