Certainly the largest number, right?

Number Theory Level 2

Which of the following numbers has the most number of positive divisors?

2 2 2^2 3 3 3^3 5 5 5^5 4 4 4^4

Pi Han Goh by Pi Han Goh , 30, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Munem Shahriar
Dec 8, 2017

  • 3 3 3^3 has ( 3 + 1 ) = 4 (3+1) = 4 divisors

  • 2 2 2^2 has ( 2 + 1 ) = 3 (2+1) = 3 divisors.

  • 5 5 5^5 has ( 5 + 1 ) = 6 (5+1) = 6 divisors.

Now, let's prime factorize 4 4 4^4

  • 4 4 = 2 8 \boxed{4^4}= 2^8 has ( 8 + 1 ) = 9 (8+1) =9 divisors
1 Helpful 0 Interesting 0 Brilliant 0 Confused
Venkatachalam J
Dec 26, 2016

A n s w e r : 4 4 , w h i c h i s e q u a l t o 2 8 ( I t h a s 9 p o s i t i v e d i v i s o r s ) A l l t h e g i v e n n u m b e r s a r e p r i m e w i t h p o w e r s a n d t h e p o w e r s a r e l e s s t h e n 8. Answer: 4^4, which \ is \ equal \ to \ 2^8 (It \ has \ 9 \ positive \ divisors)\\ All \ the \ given \ numbers \ are \ prime \ with \ powers \ and \ the \ powers \ are \ less \ then \ 8.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

2^8 has 8+1=9 positive divisors, not 8 divisors. You either forgot to account for 1 or 2^8 itself.

Pi Han Goh - 4 years, 5 months ago

Yes, you are correct I excluded divide by "1". I modified the solution. Thank you.

Venkatachalam J - 4 years, 5 months ago

Log in to reply

Wonderful!! Upvoted~

Pi Han Goh - 4 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...