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2,600 has how many positive divisors?

This topic has 5 expert replies and 0 member replies

2,600 has how many positive divisors?

Post Wed Nov 08, 2017 7:49 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    2,600 has how many positive divisors?

    A. 6
    B. 12
    C. 18
    D. 24
    E. 48

    The OA is D.

    How can I calculate the total of divisors? Is there any formula? Experts, may you help me?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 08, 2017 8:21 am
    VJesus12 wrote:
    2,600 has how many positive divisors?

    A. 6
    B. 12
    C. 18
    D. 24
    E. 48

    The OA is D.

    How can I calculate the total of divisors? Is there any formula? Experts, may you help me?
    Neat shortcut for finding the number of divisors of a given value.

    First, take the prime factorization of the number in question: 2600 = 26 * 100 = 2 * 13 * 2^2 * 5^2 = 2^3 * 5^2 * 13

    Next, add one to the exponent of each prime base and multiply the results. (Note that 13 is the same as 13^1): (3+1)(2+1)(1+1) = (4)(3)(2) = 24. The answer is D

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    Post Wed Nov 08, 2017 11:14 am
    Quote:
    2,600 has how many positive divisors?

    A. 6
    B. 12
    C. 18
    D. 24
    E. 48

    The OA is D.

    How can I calculate the total of divisors? Is there any formula? Experts, may you help me?
    Hi VJesus12,
    Let's take a look at your question.

    We are asked to find the number of positive divisors of 2600.
    In order to find number of positive divisors a number has, we find the prime factorization, and add one to all the exponents and multiply them.

    Let's write 2600 as a product of its prime factors.
    $$2600=\ 26\ \times100$$
    $$2600=\ 2\times13\ \times10\times10$$
    $$2600=\ 2\times13\ \times2\times5\times2\times5$$

    2600 is now written as a product of its prime factors.
    Let's now write the factors using exponents.
    $$2600=\ 2^3\times5^2\times13^1$$

    To find the number of positive divisors of 2600, add 1 to each exponent and multiply them.
    $$=\left(3+1\right)\left(2+1\right)\left(1+1\right)$$
    $$=\left(4\right)\left(3\right)\left(2\right)$$
    $$=24$$

    Therefore, Option D is correct.

    Hope it helps.
    I am available if you'd like any follow up.

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    Post Fri Nov 10, 2017 8:53 am
    VJesus12 wrote:
    2,600 has how many positive divisors?

    A. 6
    B. 12
    C. 18
    D. 24
    E. 48
    --------ASIDE------------------------------
    IMPORTANT: 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---------------------

    2,600 has how many positive divisors?
    2600 = (2^3)(5^2)(13^1)
    So, the number of positive divisors of 2600 = (3+1)(2+1)(1+1)
    =(4)(3)(2)
    = 24
    = D

    Cheers,
    Brent

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    GMAT/MBA Expert

    Post Fri Nov 10, 2017 1:22 pm
    If it's easier to see this visually, check out this great tutorial.

    In the future, remember that Google is your friend! In a pinch you can usually find walkthroughs of most basic formulas such as this without having to wait a few hours for an expert to reply.

    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    Post Fri Nov 10, 2017 2:53 pm
    Here's a video that explains the rule AND explains why it works: https://www.gmatprepnow.com/module/gmat-integer-properties/video/828

    Cheers,
    Brent

    _________________
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    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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