Question

express 120 as a product of its prime factors

Answer 1

120=2*60=2*2*30=2*2*2*15=2*2*2*3*5

Answer 2

Ok first Prime numbers are numbers that can only be divided by 1 and itself.

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:

\[120 = (2^3)\times (3) \times (5)\]
or
\[120 = 2\times2\times2\times3\times5\]