Question

Factor the following natural number. If the number is prime, state so.300

Answer 1

To factor a number, we need to find a prime number that divides it, then we do the division and note the prime number we have got.

Then, we repeat this with the result.

So, starting with 300, we can see that it is divisable by 2, so the first factor is 2.

Making the division, we have:

`(300)/(2)=150`

Now, we repeat with the result, 150.

150 is also divisable by 2, so we have another factor 2:

`(150)/(2)=75`

Now, 75 is divisable by 5, so 5 is the next factor:

`(75)/(5)=15`

15 is also divisable by 5, so:

`(15)/(5)=3`

And 3 is prime, so it is the final factor.

Thus, we have divided by 2, by 2, by 5, by 5 and by 3, so, the factored number is:

`300=2\cdot2\cdot5\cdot5\cdot3=2^2\cdot3\cdot5^2`