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If n=2^5*3^4*5^3*7^2*11, how many factors of...

This topic has 1 expert reply and 0 member replies

If n=2^5*3^4*5^3*7^2*11, how many factors of...

Post Wed Nov 01, 2017 8:28 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If
    $$n=2^5*3^4*5^3*7^2*11$$
    how many factors of n are there?

    A. 180
    B. 360
    C. 540
    D. 720
    E. 810

    The OA is D.

    I don't have clear this PS question. Please, can any expert assist me with it? Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Thu Nov 02, 2017 9:46 am
    AAPL wrote:
    If
    $$n=2^5*3^4*5^3*7^2*11$$
    how many factors of n are there?

    A. 180
    B. 360
    C. 540
    D. 720
    E. 810
    ----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--------------------

    Given: n = (2^5)(4^4)(5^3)(7^2)(11^1)
    So, the number of positive divisors of n = (5+1)(4+1)(3+1) (2+1) (1+1)
    =(6)(5)(4)(3)(2)
    = 720
    = D

    Cheers,
    Brent

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