Question

What is the prime factorization of 375 and of 1000?

Answer 1

`375=5^3*3`
1000=

Explanation:

Simply divide by prime numbers, and keep track of those that you use. Common prime factors in these questions are (2,3,5,7,11).
`375=(5*75)=5*(5*15)=5*5*(5*3)=5^3*3`
First we recognise that 375 is a multiple of 5. Then that 75 is also a multiple of 5, then that 15 is 5*3, which are both prime numbers.
With practice, you might recognise that `375=3*125=3*5^3`

Similarly,
`1000=2*500=2*(2*250)=2*2*(5*50)`
`=2*2*5*(5*10)=2^2*5*5*(5*2)=5^3*2^3`

Hope this helps!