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Print the prime factorization of the greatest common divisor of two numbers

Title says it all. Two input 32-bit positive integers m, n >= 2, output gcd(m,n) in prime factorization form.

Input

Command line args or 1 line of stdin okay, whatever's better for golf.

Output

Single space delimited with exponents (no additional spaces). Output nothing if the inputs are relatively prime.

Examples:

$ ./factorize 96 162
2^1 3^1
$ ./factorize 14 15
$ ./factorize 196 294
2^1 7^2

Rules

You may not use external resources, math libraries or built-in functions for factorization or GCD. Examples: Java, no java.lang.Math. ruby, no prime_division, perl, no factor, etc.

Answer*

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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Edit Summary*

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\$\begingroup\$ ⊎ is a symbol in perl? I didn't know that. \$\endgroup\$

durron597
– durron597

2014年05月11日 16:27:24 +00:00
Commented May 11, 2014 at 16:27
\$\begingroup\$ @durron597 Only Perl 6 :) \$\endgroup\$

Mouq
– Mouq

2014年05月11日 16:31:23 +00:00
Commented May 11, 2014 at 16:31

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