We can use factor trees to help us find the prime factorization of any composite whole number.


Let's take the number 4,560 for example.

We can see that the prime factors for 4, 560 are

2 · 2 · 2 · 2 · 3 · 5 · 19

To write the prime factorization in exponential form, count how many of each prime number there is.  That number will become your exponent.

2 · 2 · 2 · 2 · 3 · 5 · 19

becomes

Click here for a review on exponents.

Let's do another example.

We'll determine the prime factorization of 17, 640 and write it in exponential form.

Remember to use your divisibility rules to help make your factor tree.  The prime numbers that are left is your answer!

Let's Practice!