Prime+Factoring


 * Prime Factoring **

Numbers that can be multiplied together to get another number are its factors. For example, 4 x 3 = 12, so 3 and 4 are factors of 12. However, they're not its only factors; 1, 2, 6, and 12 are other factors of 12.

A number is prime if it cannot be divided evenly by anything except itself and 1.

For example, 5 is a prime number, because the only factors of 5 are 1 x 5 = 5.

However, 12 is not a prime number, because 1 x 12 = 12, 2 x 6 = 12, and 3 x 4 = 12.

Prime factorization means finding all the prime numbers that are factors of a number.

It's helpful to have in your head the divisibility rules for prime numbers like 2, 3, 5, and 7.

[|Divisibility Rules]

2 If the last digit is even, the number is divisible by 2.

3 If the sum of the digits is divisible by 3, the number is also.

5 If the last digit is a 5 or a 0, the number is divisible by 5.

A good basic knowledge of the multiplication table is also a help, together with familiarity with smaller prime numbers (2,3,5,7,11,13,17,19).

Let's take an example. How would you find the prime factorization of 126?

Well, one way you could start would be by noticing that 126 is even. 2 is the only even prime number, and it divides evenly into every even number. So, if we divide 126 by 2 we get 63.

126

2 63

Next we know that 6 + 3 = 9 so 63 is divisible by 3.

126 2 63  3 21

Again, 21 is divisible by 3 because 2 + 1 = 3 and because we know our facts!

126

2 63

3 21

3 7

Now we can stop since we have reached only prime numbers. The prime factors of 126 are: 2 x 3 x 3 x 7