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Find the number of ways in which 8064 can be resolved as the product of two factors?

A. 22

B. 24

C. 21

D. 20

Answer: Option B

Solution(By Examveda Team)

Total number of ways in which 8064 can be resolved as the product of two factors is 24 as below:
(1,8064), (2,4032), (3,2688), (4,2016), (6,1344), (7,1152), (8,1008), (9,896), (12,672), (14,576), (16,504), (18,448), (21,884), (24,336), (28,288), (32,252), (36,224), (42,192), (48,168), (56,144), (63,128), (68,126), (72,112), (84,96)

This Question Belongs to Arithmetic Ability >> Permutation And Combination

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Comments ( 5 )

  1. Armaan Syed
    Armaan Syed :
    3 years ago

    i think if we can take out the number of factors of 8064 which is (2^7)x(3^2)x(7^1)
    and we know that N = Xa × Yb × Zc then
    Total Number of Factors for N = (a+1) (b+1) (c+1)
    therefore for 8064 =(7+1)(2+1)(1+1) => 8*3*2 => 48 number of different factors
    so these 48 FACTORS include 1,2,3,4,6.......all the factor and if we divide it by 2 then we can say that all those different 48 factors are paired in pair of two and only those two pair whose product will form 8064.
    so we will get 24 as our answer.
    if you didn't understand then take the example given below:

    for N=90, Total Number of Factors for N =12
    1,2,3,5,6,9,10,15,18,30,45,90.
    so obviously we can say that there are 6 pairs which are: (1,90),(2,45),(3,30),(5,18),(6,15),(9,10)

  2. Bairwa Shankar
    Bairwa Shankar :
    7 years ago

    Here N=8064=(2^7)×(3^2)×(7^1) is not a perfect square so answer is (1/2)×[(7+1)*(2+1)*(1+1)]=24

  3. Bairwa Shankar
    Bairwa Shankar :
    7 years ago

    If N is not a perfect square then the number of ways of putting N as a product of two natural numbers is (1/2)×[(a1+1)×(a2+1)×...×(ak+1)]
    Where
    N=(p1^a1)×(p2^a2)×....×(pk^ak) , p_i s are primes

    ◆if N is a perfect square then the result is
    is (1/2)×[(a1+1)×(a2+1)×...×(ak+1)+1]

  4. AALOKANAD JHA
    AALOKANAD JHA :
    8 years ago

    sir,
    Any easy method to solve this problem

  5. Lalitha
    Lalitha :
    8 years ago

    give me the simple way other than this

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