Question

What is the prime factorization for 870912?

Answer 1

`870912=2^9xx3^5xx7`

Explanation:

We could do this manually:
First dividing by `2` until `2` doesn't divide evenly any more:
`color(white)("XXX")870912 = 2xx435456`
`color(white)("XXXXXXX")=2^2xx217728`
etc.
`color(white)("XXX")=2^9xx1701`
then repeat dividing by `3` until `3` doesn't divide evenly any more, and so on... to tedium.

If you have some basic programming skills you could code a program to do this process for you:

Answer 2

`870912=2^9xx3^5xx7`

Explanation:

870912 ends with the 2 digit, therefore is divisible 2. This happens when the last digit is 0,2,4,6 or 8.

870912/2=435456
435456/2=217728
217728/2=108864
108864/2=54432
54432/2=27216
27216/2=13608
13608/2=6804
6804/2=3402
3402/2=1701

The sum of digits of 1701 is multiple of 9, so this number is divisible at least twice by 3 (if it were multiple of 3 but not of 9, it would mean divisble by 3 just once):

`1701//3^2=189`

The same happens with 189:

`189//3^2=21`

We know that `21=3xx7`

Counting all the factors we will get

`870912=2^9xx3^5xx7`