Chapter 4.1, Problem 1E

To determine

To find how to write the prime factorization of a number.

Explanation of Solution

Given Information: To write the prime factorisation of a number.

Formula used: "Prime Factorisation" is finding which prime numbers multiply together to make the original number.

Proof:

Example: What are the prime factors of 12 ?

It is best to start working from the smallest prime number, which is 2, so let's check:

  $12÷2=6$

Yes, it divided exactly by 2!

But 6 is not a prime number. Let's try 2 again:

  $6÷2=3$

Yes, that worked also. And 3 is a prime number, so the answer:

  $12=2\times 2\times 3$

As visible, every factor is a prime number, so the answer must be right. 

Note: $12=2\times 2\times 3$ can also be written using exponents as $12=2^2\times 3$