Divisors strange

Hello everyone.

I have posted here one of my observations regarding the divisors of some numbers.

I don't know if it is already a law in Mathematics or not but here I go...

I noticed that the even composite numbers which have 6 distinct divisors(including 1 and itself) ,the product of these divisors always came equal to the cube of that number.

e.g. 12= $1*2*3*4*6*12$ = $12^{3}$

similar examples are 18,20,28,32,42,44..................

2nd part

I also noticed that even composite numbers with 8 distinct divisors,the product of the divisors was equal to $n^{4}$

e.g. 24= $1*2*3*4*6*8*12*24$ = $24^{4}$

similar examples are: 30,40,......

#NumberTheory

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

Check out Product of Factors.

Calvin Lin Staff - 5 years, 12 months ago

Oh! I had not read that nor did I knew.Thank you very much,now I have came to know that it already exists.

Sir,I have some more findings in probability and geometry which I am not sure that if it already exists or not. Can I post it on Brilliant?

Siddharth Singh - 5 years, 12 months ago

Sure. Do you best to provide an explanation of why the statement is true, or what you've tried to demonstrate that it is true.

Calvin Lin Staff - 5 years, 12 months ago

If u r sure that this is always correct than congrats....proud of u!!!

sarvesh dubey - 5 years, 12 months 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}`	$\boxed{123}$