Question

Express 120 as a product of its prime factors.

Answer 1

120 = 2 x 2 x 2 x 3 x 5 or 120 = 2^3 x 3 x 5

Answer 2

By the Fundamental Theorem of Arithmetic, all number can be expressed as a product of prime numbers.

So naturally, lets divide 120 by an easy prime number.
We know that 120 is even, so lets try 2 120/2 = 60 lets keep dividing it by two until it becomes odd or prime 60/2 = 30 30/2 = 15 now lets see, what are some factors of 15?

Well the obvious ones are 3 and 5, both of which are prime. So now we can just count up how many times we divided it by 2

120/2 = 60 60/2 = 30 30/2 = 15 and 15 is just 3 x 5, so:
120=(23)×(3)×(5)
or
120 = 2 × 2 × 2 × 3 × 5