Aptitude Discussion

Q. |
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 |

**Solution:**

Option(**B**) is correct

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).

**Edit:** For an alternative solution, check comment by **Shubham.**

**Edit 2:** For the explanation on the alternative solution, check comment by **Lee.**

**ABHIJEET**

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**GAURAV AGRAWAL**

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There are total 48 factors....agree.........but it requires 2 factors for product so ans is 24

**Sanket Singh**

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48 must be the right answer !!

**Rounak**

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try for the formula for number of factors as a product of two factors...(p+1)*(q+1)*(r+1)*0.5. where p,q,r are the powers of the prime numbers a,b,c.

**Shivang**

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how is this question related to permutation and combination??

**Lohitha**

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can anyone tell how in ans those nos 1,8064 etc obtained

**Isha**

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adding one to the degrees of the factors obtained and multiplying them is the basic way of finding the number of factors or divisors the number can have

find the factors of the number

find the degrees of each one of them

add 1 to every degree

now multiply

this is how you can find the number of divisors or factors of any given number

**Saravanan**

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can you explain what methodology used to find (7+1)*..... i am confused

**Shubham**

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$8064=2^7*3^2*7$

number of factors $=(7+1)*(2+1)*(1+1)=48$

no.of ways of writing 8064 as a product of two $= \dfrac{48}{2}=24$

I still don't UNDERSTAND how that METHOD works I did it manually

do you use prime numbers?

@Nyiko, it is a formula you will find in numbers. If you want to find the no of factors of say 6, find its factors with degrees:

6= 2^1*3^1 right, hence: no. of factors of 6= (1+1)*(1+1)=4

which works out as the factors of 6 are= 1,2,3,6.

So, formula stated above says the number of factors of n is the product of (the degree of its factors plus one).

why we have divided 48 by 2??

**Adarsh**

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u..ppl r doin a god job.just wanted to know a easier way to solve this type of problem..thank you.

8064 has 48 total factors.. and each factor can be written in the groups of (1,8064), (2,4032), (3,2688), (4,2016), (6,1344) and so on.. total 48. for 2 factors form 1 group so 48 factors will form 24 groups each containing 2 factors.