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Basic Operations

Basic Operations

At a Glance - Prime Factorization

Prime factorization is the process of breaking down a number into its prime factors.

Say what?

Ok, let's break that statement down:

  • Prime number: a number that is only divisible by one and itself. 
    • 3 is only divisible by 1 and 3, so (spoiler alert!) it's prime
    • 4, however, is divisible by 1, 2, and 4. It's not prime
    • The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
  • Factor: a number that can be divided into another number. For example 1, 2, 3, 4, 6, and 12 are all the factors of 12.

How to Do It

Here's a nice way to visualize factors: a factor tree. Start by finding any factor of the number at top. Circle the factor if it's a prime number. That branch ends right there. Otherwise, keep factoring each branch down until all of the branches end in circles (that is, prime numbers).

You can check your answer by multiplying all the prime factors together.

Prime Factorization Example 1

Here are two ways to prime factorize 32.

Factors of 32Factors of 32

Prime Factorization Example 2

And here's 60.

Factors of 60Factors of 60

Prime Factorization Example 3

And 132.

Factors of 132Factors of 132

Prime Factorization Exercise 1

Prime factorize 120.

Prime Factorization Exercise 2

Prime factorize 375.

Prime Factorization Exercise 3

Prime factorize 47.

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