Fractions:

Prime Factorization

Learning how to find the prime factorization of a number is important when we start learning about fractions. This is especially important when we start reducing fractions. Here are some vocabulary words that will help you with this lesson:

Factor = a number that divides evenly into another number (Example: 3 is a factor of 12 because 12 ÷ 3 is a whole number).
any number where the only factors are 1 and itself (Example: 11 is a prime number. There is no other number other than 1 and 11 you can divide it by that will give you a whole number).

The first video will explain more about primes and how to determine if a number is prime.

Video Source (05:52 mins) | Transcript

Once we know what prime numbers are, we learn that each number is made up of smaller prime numbers. Breaking a number into the primes that make it is called its prime factorization. Every number has a prime factorization. For prime numbers, their only factors are themselves and 1. This video will show how to find the prime factorization of a number and work through a couple of examples.

Video Source (06:44 mins) | Transcript

It’s helpful to memorize some of the prime numbers, which will make it easier to find prime factorization in future problems. Use this chart to memorize the primes up to 20. Be familiar with the prime numbers up to 100.

Additional Resources

Khan Academy: Prime Numbers (08:12 mins, Transcript)
Khan Academy: Prime Factorization (04:08 mins, Transcript)
Khan Academy: Prime Factorization Examples (03:48 mins, Transcript)

Practice Problems

Find the prime factorization of the following numbers:

Solutions

21 = 3 × 7 (Written Solution)

3 × 7 = 21; and 3 and 7 are prime factors. The prime factorization of the number 21 is 3 and 7
13 = 1 × 13 (Written Solution)

The definition of a prime number is any number where the only factors are 1 and itself.

The only factors of 13 are 1 and itself, 13. The prime factorization of 13 is just 13.
30 = 2 × 3 × 5 (Solution Video | Transcript)
12 = 2 × 2 × 3 (Written Solution)

First, find the factors of 12. Here we show a few ways to factor 12. It can be factored as either 4 × 3 or 6 × 2

The numbers 3 and 2 are both prime, but 4 and 6 are not.

Next, find the factors of 4 or 6. Notice how the prime factorization of 12 is 2 × 2 × 3 whether the starting factors were 4 × 3 of 6 × 2. The prime factorization is the same.
54 = 2 × 3 × 3 × 3 (Written Solution)

54 is an even number so we know it is divisible by 2.

2 × 27 = 54

The number 2 is prime, but 27 is not, so we must find the factors of 27.

27 is divisible by 3

3 × 9 = 27

The number 3 is a prime number, but 9 is not prime, so we must find the factors of 9.

9 is also divisible by 3

3 × 3 = 9

The number 3 is a prime number so there are actually two more 3’s in our prime factorization.

Now we go back and find all the prime numbers in the factorization of 54.

54 = 2 × 3 × 3 × 3
250 = 2 × 5 × 5 × 5 (Solution Video | Transcript)