In math tutoring, prime numbers and prime factorization are receiving fresh attention.  We’ll briefly look at the concepts.

Before we talk about prime numbers, let’s define factor.  In math, a factor is a number that divides into another number with no remainder.  Therefore, 4 is a factor of 12; 7 is a factor of 14.

We also need to define product.  A product is the answer to a multiplication.  Therefore, the product of 2 and 5 is 10.  We could also say that 36 is the product of 9 and 4.

A prime number is a number with only two factors:  itself and one.  The number 1 is not prime, since it only has one factor:  1.  However, 2 is prime, as are 3, 5, 7,11,13, 19, and so on.  Note that 9 is not prime, since 9 has 3 as a factor besides itself and 1.

The prime factorization of a number is the number stated as a product of primes.  Each number has a unique prime factorization, if you discount the different orders.  The prime factorization of 10 is 2×5.  The prime factorization of 48 is 2x2x2x2x3, or 2⁴x3.  Note, once again, that the prime factorization only includes prime numbers as defined above.

To illustrate how to get the prime factorization of a number, you might use the ancient “factor tree” method.  For example, imagine you need the prime factorization of 396:

Notice each path ends with a prime number.  Collecting them all gives 396=2x2x3x3x11, or 396=2²x3²x11.

We’ll explore some uses of the prime factorization in future posts.

Jack of  Oracle Tutoring by Jack and Diane, Campbell River, BC