Hello and welcome to Prime Factorization.
In this video you will learn that prime factorization
is the list of prime numbers that, when multiplied, equal the original number.
Prime numbers are numbers that can be evenly divided only by 1 and by the number itself.
Prime numbers can not be divided by other numbers.
Prime factorization is finding which numbers multiply together to make the original number.
Let's compare a prime number and a number that is not a prime.
3 is a prime number.
3 can only be divided evenly by 3 and 1.
6 is not a prime number.
6 can be divided by 6 and 1, but also by 2 and 3.
Did you notice how this diagram looks a lot like a tree?
In fact, the name for this diagram is a, "Factor Tree."
This is a list of some prime numbers.
2, 3, 5, 7,
11, 13, 17, 19,
23, 29, 31, 37,
41, 43, 47
There are many more prime numbers.
Each of these numbers is prime because it can only be divided by itself and 1.
Some numbers only have 2 prime factors.
For instance, the prime factors of 33 are 3 and 11.
The prime factors of 21 are 3 and 7.
Other numbers have more prime factors.
What numbers do you typically think of when you think of the factors of 12?
It might be 3 and 4.
Or, 2 and 6, because 3 x 4 = 12,
and 2 x 6 also equals 12.
Now 2 and 3 are prime numbers, but 4 and 6 aren't.
When finding a prime factorization, we need to break down all of the factors to prime numbers.
The prime factorization of 12 is 2 x 2 x 3.
2 x 2 x 3 = 12.
Let's try 48.
Now you might immediately think of 8 x 6 = 48.
Let's draw out the same diagram, or factor tree.
This makes the prime factors 2 x 2 x 2 x 2 x 3.
Understanding prime factorization will help you to solve math problems
where you'll need to break larger numbers down.
But, be careful.
Factorization and prime factorization are two different things.
To learn about factorization, watch the video called, "Factoring Numbers."
You can practice finding factors and prime factors on our fun online games and quizzes.
Remember to always be clever.