Question

How do you write 720 as a product of its prime factors?

Answer 1

`720=2xx2xx2xx2xx3xx3xx5`

Explanation:

To write any number as a product of its prime factors, we should find all those prime numbers which when multiplied together form the number. Note that in such factorization, prime numbers can get repeated as well, but what is important is that

(1) all numbers are prime

(2) and their product is given number

Hence, we should divide the given number consistently by prime numbers starting with `2`, which is first prime number and continue till all factors are prime numbers.

Before we try this for given number `720`, let us list first few prime numbers, which are `{2,3,5,7,11,13,17,19,23,29,...}`

Now `720`

= `2xx360` (and as `360` can be divided by `2` again)

= `2xx2xx180`

= `2xx2xx2xx90`

= `2xx2xx2xx2xx45`

= `2xx2xx2xx2xx3xx15`

= `2xx2xx2xx2xx3xx3xx5`

As now we have all prime factors, the process is complete and prime factors of `720` are `2xx2xx2xx2xx3xx3xx5`.

Answer 2

`720 = 2^4 xx3^2 xx5`

Explanation:

You can do the "ladder method"of continuous short division, making sure that you only divide by prime numbers.

I prefer to just use 2 factors to start with and then split the factors again and again until they are all primes.

This method is quick, easy and effective, but it requires a solid knowledge of the times tables.......

`720 = color(red)(72)xxcolor(blue)(10)`

= `color(red)(8xx9) xx color(blue)(2xx5)`

= `color(red)(2xx4 xx3xx3)xxcolor(blue)(2xx5)`

=`2xx2xx2xx3xx3xx2xx5`

=`2^4 xx3^2 xx5`

You can start with any pair and you will end up with the same result.

`720 =80xx9 = 36xx20 = 12xx60 =8xx90 = 120xx6` etc

`color(magenta)("Or if you prefer the visual approach use a factor tree:")`