Prime factorization is a method of breaking large numbers down into smaller prime numbers that when multiplied together equal the original number. Any non-prime number can be broken down into its prime factors, but breaking down these numbers is hard! This tool will make it easier and help you check your work when you need to do it by hand.

To break down a number (like 462) into its prime factors by hand you would:

• First check to see if 462 is divisible by the smallest prime number over 1, which is 2.
• If your number is divisible by 2, you would write 2 and 462/2 or 231 down.
• Then you would take the 231 and try to divide by 2 again.
• Since 231 is not divisible by 2, you would then check the next highest prime number, which is 3. 231 is divisible by 3 (remember your divisibility tests: 2+3+1 = 6 which is divisible by 3), so you would write 3 down as the next prime factor, and also write down 231/3 which equals 77.
• 77 is not a prime number, so we need to keep going. You will take 77 and try to divide by prime numbers again. Both 2 and 3, plus 5, the next prime number, do not divide evenly into 77, but 7, the next prime number after 5, does divide evenly. 77/7 equals 11 so you would write 7 and 11 down.
• When we look at 11, since it is a prime number, we’re done! The prime factorization of 462 is thus 2,3,7,11.
• Try putting our original number into this calculator and you’ll see that we get the same result. Huzzah!