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----ASIDE----------------------- If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40 -----ONTO the question--------------------------

16,000 = (2^7)(5^3) So, the number of positive divisors of 16,000 = (7+1)(3+1) = (8)(4) = 32

Cheers, Brent
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Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

----ASIDE----------------------- If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40 -----ONTO the question--------------------------

16,000 = (2^7)(5^3) So, the number of positive divisors of 16,000 = (7+1)(3+1) = (8)(4) = 32

Cheers, Brent

I understand this concept but just for in depth clarity please claarify that the above method will list all the factor including negatives and positives ? so I divided 32/2 to get 16 positive and 16 negative factors ...please clarify?

Re: The number 16,000 has how many positive divisors? [#permalink]
16 May 2018, 04:22

1

This post received KUDOS

Expert's post

kruttikaaggarwal wrote:

Hwo do we get to 16,000= (2^7)(5^3) Is it trial and error?

Here's our video explaining how to find the prime factorization of a number:

_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails