Searching for Factor Strings Some numbers can be written as the product of several different pairs of factors, like 24. It is also possible to write this number as a prime factor string, using only prime numbers. Today, we will learn two strategies for finding all the prime number factors for a given product.

Division Strategy Using halving, you can repeatedly divide a product by two over and over again until you reach an odd product. Once you reach an odd product, try dividing the remaining amount by the next prime number, 3. If it is not divisible by three, move on to the next prime #, 5. Remember all numbers with a 5 or 0 in the ones place will be evenly divisible by 5. Continue with this until you only a prime number factor pair remaining.

Strategy #2: Factor Trees First find a factor pair for the given product. Break each factor into two more factors. Continue until the bottom row has only prime factors.