How to get the prime factors of a number?
Let us first define some terms before discussing our topic.
Factors- are numbers we can multiply together to get another number.
For example what are the factors of 12?
2x6=12, so 2 and 6 are factors of 12 .
Also, 3x4 = 12 so, 3 and 4 are factors of 12.
Another is 1x12= 12, 1 and 12 is also a factor of 12.
Prime number- any number that can only be divided evenly by either itself or by the number 1 is a prime number. Only whole numbers that are larger than 1 can be considered prime.
Prime factorization-is simply the act of determining which prime numbers can be multiplied together to make the given number, and prime factors is the term used to define these numbers.
Lets have an example:
What are the prime factors of 18? One way to figure out the answer is to start from the smallest prime number and work up from there. Not sure how to figure out if a number is prime? Try to break down the original number into any factors that are easier to work with, then break those factors down into prime numbers. Lets answer the example 18 can easily break down into 6x3, 3 is a prime number because it can be divided evenly by either itself or by the number 1, six can be break down into 2x3 and 2 is a prime number as well as 3, so the prime factors for 18=2x3x3.
Using the above method can be easier when it is visually represented by a factor tree. Lets use a slightly harder example, Let us find the prime factors of 56.
How to get the prime factors using a factor tree:
1. Write the given number to begin.
2. Choose to numbers which multiply to the given number.These two numbers will form your first two branches.
3. If the number is prime, box it, you will not do anything else to this number.
4. If the number is composite, find two numbers which multiply to the number. These new numbers will for new branches.
5. Continue until all numbers will ended in prime numbers.
Factor Tree Method
The prime factors of 56= 2x2x2x7
Another method is the birthday cake method. Lets use the given example, find the prime factors of 56.
How to get prime factors using birthday cake method?
1. Write the given number to begin.
2. Find a prime number that divides evenly into the given number. Write this number beside the given number.
3. Divide the given number by the prime number and write the result as the next layer of the cake.
4. Find a prime number that divides evenly into the new number.
5. Repeat the process until you end with a prime number.
Birthday Cake Method
The prime factors of 56= 2x2x2x7.
Another examples:
Find the prime factors of 75 using the Factor Tree Method
Find the prime factors of 660 using the Birthday Cake Method.
The prime factors of 660= 2x2x3x5x11.
Find the prime factors of the following using Factor tree or birthday cake method.
1. 125
2. 248
3. 322
