- Knowing rules for divisibility by 2, 3, 4, 5, 9 and 10 can be very helpful in finding the prime factorization of numbers.
- When students seek to find the prime factorization of a number like 48, the process will be quicker and probably easier for them if they start with the composite factors like 6 and 8 than with a prime factor like 2 and 24.
- Recognizing numbers which are the "basic-fact" products (the product of two numbers from 2 to 10) is also useful. For example, if the students are asked to find the prime factorization of numbers such as 27, 48, 56 and 63, knowing that they are part of the basic facts for multiplication can help them find the factors much more quickly.
- When introducing the concept of prime factorization, work with two-digit numbers the first day and extend it to simple three-digit numbers in which they can apply their rules for divisibility like 240 or 189.
- When students believe they have completely factored a number, have them check their answers by multiplying the factors to see if they get the original number.