Math, asked by shraddha9168, 1 year ago

Find the total number of divisors of 3072 a question of permutation and combination

Anonymous: hey can I answer without using combinatorics?

shraddha9168: r u solving it by factorization method?

Anonymous: yep

shraddha9168: yeah solve it

shraddha9168: i am getting 44

shraddha9168: :(

Anonymous: ok trying wait ! actually imma in class 10 so i don't remember combinatorics since fitjjee exam .................. it can be 44 wait

shraddha9168: no it is 22

shraddha9168: i checked option

shraddha9168: but i am getting 44

Answers

Answered by Anonymous

The number given is 3072.

With a little effort we see that 3072 = 1024 × 3

= 2¹⁰ × 3¹

Total prime factors is 10 + 1 = 11

Number of prime factors involved = 1 + 1 = 2 [ 2 and 3 ]

So, total divisors are 11 × 2 = 22

The total divisors are 22

Hope it helps u:-)

____________________________________________________________

shraddha9168: yes

Anonymous: wait i am editing my answer

shraddha9168: ok

shraddha9168: i got the answer in much simpler way

shraddha9168: when we factorize we get 2 raised to 10 multiplied by 3 raised to 1

Anonymous: yes

shraddha9168: then we add 1 to the powers i.e 10+1=11 & 1+1=2

shraddha9168: then multiple 11 ×2=22

Anonymous: yes me too same approach

shraddha9168: ok dear

Answered by shashank4212

My Attempt: Since they are divisible by 15 and are even, 2 and 5 have to included from the numbers prime factors.

2079000=23⋅33⋅53⋅7⋅11

Therefore, the number of divisors should be

2⋅2⋅(3+1)⋅(1+1)⋅(1+1)

But however this answer is wrong.

Any help would be appreciated.

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