# Prime Factors - a Matlab script

This program lists the prime factors (PFs) of an integer. It will test neither 0 nor 1.

It is well known that PFs of a positive integer are the primes that divide into that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization.

Matlab has some functions for this purpose, too.

Here’s the full Matlab script:

% Clears variables and screen
clear; clc

z = input('Enter your positive number: ');

% Loops to test all integers (2 through z) as PFs
for i = 2 : z
s = 0;
% Is z/i an integer? Is the remainder 0?
while z/i == floor(z/i)
z = z/i;
s = s + 1;
end

% A PF is found and displayed
if s > 0
str = [num2str(i)
'^' num2str(s)];
disp(str)

% If z = 1, no more divisions are necessary,
% thus breaks the loop and quits

if z == 1
break
end
end

end

Example 1:

What are the prime factors of 49?

Run the code above and enter your number…

2^1
3^2
5^1

This means that 90 = 2 x 32 x 5

Example 2:

2^1
3^1
5^1
13^1

This means that 390 = 2 x 3 x 5 x 13

Matlab has at least 3 built-in functions related to PFs.

a) 'factor(x)' returns a vector containing the PFs of x. For example:

factor(390), results in

ans =
2 3 5 13

b) 'primes(x)' is a row vector of the primes less than or equal to x. For example:

primes(10), results in

ans =
2 3 5 7

c) 'isprime(x)' is true for prime numbers. For example:

isprime(10) results in

ans = 0

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