To find prime numbers, use factorization to break down numbers and test whether they are prime or not. Numbers that are prime only have themselves and 1 as their factors; if they break down into other smaller numbers, they are not prime.
- Look for even numbers that have a factor of 2
Check if the number is even by looking to see if the last digit is 2, 4, 6, 8 or 0; if it is, the number is not prime, unless the number is 2. Remember that even numbers are divisible by 2 and so are not prime.
- Look for numbers that have a factor of 3
Add the digits of the number together. Divide the sum by 3; if you get a whole number, the original number is divisible by 3, which means that it is not prime. For example, for the number 771, add 7 + 7 + 1 to get 15. 3 divides evenly into 15 five times, meaning that 771 is not prime.
- Test for a factor of 5 or 7
Look at the number's last digit; if it is a 5 or 0, the number is divisible by 5 and therefore is not prime, with the exception of 5 itself. Take the last digit off, multiply it by two, and subtract it from the shortened original number, then repeat the process until only one digit is left. Consider the example 1,645: 164 - 10 = 154; 15 - 8 = 7. Remember that if the final answer is 0 or 7, the original number if divisible by 7 and so is not prime, with the exception of 7 itself.
- Use a factor tree to check your work
Put the original number at the top of a factor tree, and use your divisibility tests and a calculator (if necessary) to break your number down into its factors. Remember that prime numbers only result in the number itself and 1 as the two forks of the factor tree.