A prime factor is just a factor of a number that happens be prime. More info on prime numbers here.
Now finding prime factors of a non prime number, isn’t too different to trying to find factors of a number in general.
Except we’re specifically looking for factors that are prime numbers.
With prime factorization of a number, we’re looking to re-write a number as the product of prime factors multiplied out together.
Prime Factorization of a Number Examples
1.1
We can consider a random number as an example, let’s say 68.
The approach we use is to keep carrying out a division by prime numbers, until we get an answer is also prime number.
Look to start off by trying to divide the number by the lowest prime number, which is 2.
1) 68 ÷ 2 = 34
2) 34 ÷ 2 = 17
We’ve reached a prime number after two divisions.
Now if we multiply together the last prime number obtained as an answer, with the prime numbers that have been used to divide at each stage, this should result in the original number at the beginning.
With this case, it was only 2 that was used to divide at each stage.
But it was still used a total of two times in order for us to obtain the prime number of 17.
2 × 2 × 17 = 4 × 17 = 68
This new sum can be simplified with an exponent/power, to result in the prime factor form for 68.
22 × 17 = 68
In this form, 2 and 17 are factors that are prime.
That completes the prime factorization of 68.
1.2
Let’s try prime factorization with 75.
1) 75 ÷ 2 = 37.5 Doesn’t divide exactly, so try to start with the next prime number instead, 3.
2) 75 ÷ 3 = 25
3) 25 ÷ 3 = 8.33 Doesn’t divide exactly, so try with the next prime number after 3, which is 5.
4) 25 ÷ 5 = 5 => 5 is a prime number.
3 was used at one stage of exact division, and 5 was also used at one stage before obtaining the prime number of 5 as an answer.
3 × 5 × 5 = 9 × 5 = 75
This can be written as 3 × 52 = 45.
1.3
We can try the prime factorization of a number that is larger, 284.
1) 283 ÷ 2 = 142
2) 142 ÷ 2 = 71 => 71 is a prime number.
2 was used at two stages of exact division before obtaining the prime number of 71 as an answer.
2 × 2 × 71 = 4 × 71 = 71
This can be written as 71 × 22 = 248.
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