Determine the smallest prime factor of the number.
If the number is even, 2 is the smallest factor.
If the sum of the digits in the number are divisible by 3, the number is divisible by 3 (ie: 15; 1+5=6; 6 is divisible by 3, so 15 is also divisible by 3)
If the number ends in a 0 or a 5 it is divisible by 5.
Divide the number by the smallest prime factor.
Determine if the second factor found is prime or can be broken down further.
The same rules apply from Step 1.
If the second factor is not prime, divide it by its smallest prime factor.
Repeat Steps 2 and 3 until all factors you find are prime.
List all of the prime factors that you found.
For example, if you divided by 2 a total of three times, and the last time got a 3, the prime factors are 2, 2, 2 and 3.
Check yourself by multiplying the prime factors together. If the product is the same as the original number, your factors are correct.
Determine the smallest prime factor of 12.
12 is even; the smallest prime factor is 2.
Divide by the smallest prime factor.
12/2 = 6
Determine if the second factor is prime or can be broken down further.
6 is NOT prime. It is even, so 2 is the smallest prime factor.
Divide the second factor by its smallest prime factor.
6/2 = 3
Determine if these factors can be broken down.
2 and 3 are both prime. They cannot be factored any further.
The factors of 12 are: 2, 2 and 3.
Check yourself by multiplying the prime factors together.
2x2x3 = 12. 12 is the original number we factored, so these factors are correct.
Determine the smallest prime factor of the number.
25 is NOT even.
2+5 =7; it is NOT divisible by 3.
25 ends in a 5. It is divisible by 5.
Divide the number by the smallest prime factor.
25/5 = 5.
Determine if the second number found is prime or can be divided further.
We noted that 5 is a prime number, so it cannot be broken down any further.
List the prime factors found.
5 and 5 are the factors of 25.
Check your work by multiplying the factors.
5x5 = 25. 25 is the original number we factored, so these are the correct factors.