Prime Factorization

Prime Factorization

Recall: What is a factor, and how is prime and composite numbers connected to it?

Factors are numbers you can multiply together to get a number. Example: the prime factors of 8 are 1,2,4,8 because 4×2=8 and 8×1=8. A prime number has 2 factors only, 1 and itself. A composite number has more than 2 factors. Always remember the prime factors of a number are always prime numbers. 

What is prime factorization?

Prime factorization is expressing a composite number as a product of it's prime factor. There are two methods to do this. One is factor tree and the other is division method.

Factor tree

In factor tree, you solve from top to bottom, hence the name, factor tree. The composite number you want to factorize stays on top, then you keep dividing it until you are left with prime numbers.

Here is a picture showing factor tree:

The final answer is written as 60=2×2×3×5. It can also be written as 60=2²×3×5, in index notation.

Index notation will be our next lesson.

Division Method

In division method, you divide the number you want to factorize by prime numbers. Keep dividing until you get a prime number, or a number that cannot be divided.

Here is a picture showing division method: 

As you can see, the final answer is also 60=2×2×3×5. t can also be written as 60=2²×3×5, in index notation.

Index notation will be our next lesson.

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