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Working Out the Prime Factors of a Number

Updated on May 6, 2013

To work out the prime factors of a number you have to first of all learn two things, what a prime number is and how to find factors of a number - and I hope this hub will help you easily understand both of these.

I have split the explanation into 3 parts; Prime Numbers, Factors and finally Prime Number Factors which will explain the process of how to find them.

Prime Numbers

A Prime Number is a number that can be divided only by itself or 1 and leaves a whole number as the answer.

So the only even prime number is 2 (because it can only be divided by itself and 1).

3 is also a prime number, you can't divide it by anything else other than itself or 1.

Now 4, 4 is not a prime number because it can be divided by 2, which also means that all even numbers (except for 2) are not prime numbers. So (except for 2) any number ending in 0, 2, 4, 6 or 8 is an even number and cannot be a prime number.

You may need to read that through a few times before you get it, basically if it's an even number it's not a prime number unless it's the number 2. And if you can divide the number, by anything other than itself, let's take the number 15 for example, you can divide it by 5 and you can divide by 3 so that is not a prime number.

Here is a list of all the prime numbers from 2 to 1,000.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.

Only when you understand what a Prime Number is can you take the next step and that is understanding what a Factor is.


Factors are easily understood, they are numbers that you multiply together to get another number, so ...

2 x 6 = 12

So the numbers 2 and 6 are factors of 12.

Prime Number Factors

Now you need to apply the same principle but using only prime numbers.

So although 2 and 6 are factors of 12, if you want prime factors of 12 then 6 just doesn't cut it, it's not a prime number so it will never be a prime factor, it's a bit like a private club and 6 can't come in.

Of course you already know from your maths at school that 2 x 6 is 12 but if you have a number that you don't know then it is always best to start working from the smallest prime number, which is 2, so the process would be:

Step 1: 12 ÷ 2 = 6

Step 2: decide whether your answer is a prime number

Step 3: 6 is not a prime number, so let's try 2 again

Step 4: 6 ÷ 2 = 3

Step 5: decide whether your answer is a prime number

Step 6: 3 is a prime number

So the numbers you used to get to 12 are all the prime numbers 2 and 3, but you had to use 2 twice (see Step 1 and 3 above) so the answer you are looking for is:

12 = 2 x 2 x 3

(This can also be written as 12 = 2² x 3

I hope this is clear, if not please let me know what confuses you that I've written and I will amend it.


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