Question

if n = 411 + 412 + 413 + 414 then how many positive factors of n are there?

Answer 1

Answer:

24

Step-by-step explanation:

Here we need to understand, what is positive factor is ?

Answer : A factor is any number that divides evenly into another number. meaning lets say number 10 for example so 1, 2, 5, 10 are four positive factors of 10 cause we can evenly divide 10 as per below,

1*1*1*1*1*1*1*1*1*1 = 10

2*2*2*2*2 = 10

5*5 = 10

10 = 10

So 1,2,5,10 are positive factor of 10.

Now,

N = 411 + 412 + 413 + 414

we will divide this four number as per below ,

so, 411 + 414 = 825

and 412 + 413 = 825.

So, given number is 825×2=1650     ...i.e. 411+412+413+414

To prime power factories it, I factories by trivial non-prime factors.

now, we make factor of 1650  

i.e.

=50*33  

=2*25*3*11  

Number of factors are product of all (powers+1) in Prime Power Factor.

So number of factors here are  2×2×3×2=24 .

Factors are  1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 150, 165, 275, 330, 550, 825, 1650