A little puzzle involving factors of Integers

January 22nd, 2008 | Categories: general math | Tags:

What is the only integer below 500,000 that has exactly 13 factors (including 1 and itself)? What is the next integer with this number of factors? For extra credit list all of the factors of these two numbers.

Finally, what is the only integer below 10 million that has exactly 23 factors (including 1 and itself)?

  1. January 23rd, 2008 at 14:34
    Reply | Quote | #1

    4096 has factors 1,2,4,8,16,32,64,128,256,512,1024,2048,4096
    531441 has factors 1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441

  2. VolMike
    August 5th, 2008 at 12:34
    Reply | Quote | #2

    It’s obvious: 2^12 and 3^12.