2. Write 120 as a product of its prime factors. Show your work for full marks. [

Answer 1

To find the prime factors of 120, we start by finding the smallest prime number that divides 120 evenly, which is 2.
120 ÷ 2 = 60

So we have factored out a 2 and are left with 60. We repeat the same step for 60.
60 ÷ 2 = 30

Again, we have factored out a 2 and are left with 30. We repeat the step for 30.
30 ÷ 2 = 15

We have factored out another 2 and are left with 15. Now we try dividing by the next prime number, which is 3.
15 ÷ 3 = 5

Finally, we have factored out a 3 and are left with 5. At this point, we can see that 5 is a prime number, so we have completed the factoring.

Putting it all together, the prime factors of 120 are 2 x 2 x 2 x 3 x 5 = 2^3 x 3 x 5.