Prime Factors

Is there a theorem that describes how many prime factors a number has? And does this this theorem have a solution on how to find them?

#NumberTheory #PrimeFactors #HelpMe! #Math

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

How many distinct prime factors or how many non-one primes multiply out to it? Does 12 have 2 prime factors (2 and 3) or 3 (2, 2, and 3)?

Peter Lynn - 8 years, 1 month ago

You just jumped the gun on me. I was going to say that I doubt that there is such a solution. If there were, it would be a test for primality. Tests for primality are expensive to computer. The simplest one is to factor the given number, which would answer your question but is computationally difficult for numbers of even moderate length.

Look into the Euler Totient Function, and notice that computing it for large numbers seems to call for factorizing those numbers. My COMPLETE GUESS is that there is no better theorem for counting the prime factors than factorizing the number and counting them.

Have you read something like the overview in Wikipedia on primality tests? They are not simple.

Since the above is a guess, does anyone out there actually know the answer?

Peter Lynn - 8 years, 1 month ago

The second one. I'm interested on how to find those factors for any given number. And can I also add another question? Is there a way on finding whether a given number is prime?

Gabriel Kong - 8 years, 1 month ago

Haha. The answer to my last question would seriously have a great impact on math theory, worth asking anyway. Haha. About the theorem, I see that we have a similar opinion. I just shot the question in hope that there's some deep math theory about prime factors which might be beyond my knowledge. Thanks a lot by the way.

Gabriel Kong - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$