How to Use Subsequent Division in Prime Factorization

Factorization diagrams are often called factor trees because of their branch-like structure.

Prime numbers are numbers that have two factors: one and the number itself. It is important to remember the "two factors" element of the definition because the number 1 is not prime even though it is only divisible by itself and one. Similarly, zero is not prime. A factor is a smaller number that divides evenly into a larger number. Prime factorization is a process by which a number is expressed as the product of its prime factors.

Instructions

1. Divide the number being factored by any number that will go in evenly. (For example, if the number is 240, an obvious factor to pull out would be 10 since the number 240 ends in a zero.) Draw two lines down from the number being factored, one pointing toward the left and the other pointing toward the right.

2. Write the number that you factored out at the bottom of the left line. At the bottom of the right line, write the quotient that remains after you divided out the factor. (In the above example, you would write a 10 and a 24.) Repeat this process every time you factor out a number.

3. Divide even numbers at the end of branches by 2. Repeat this process until you get an odd quotient for each branch. At this point, every number at the end of a branch should either be the number 2 or an odd number.

4. Try dividing each odd number by all the prime numbers that are less than the number's square root. For any that go in evenly, factor them out. Repeat this process until you are left only with prime numbers at the end of each branch. You will know that a number is prime when none of the prime numbers that you try go in evenly.

References

• "The Official SAT Study Guide"; The College Board; 2006