Primes, Factors and more

When it comes to the math section of the SAT, primes and factors are another basic math area that people fear although they shouldn't. While there may be tricky questions on the SAT, those that understand primes and factors will have no problems answering the questions found on the SAT math section. To help, we are going to have a basic lesson on factors, prime numbers and other areas that may be found on the SAT. Luckily, these are very simple math concepts that, once mastered, are easy to do no matter how the question is phrased.  Prime Numbers A prime number is one that only has two factors - itself and the number one (1). These two numbers are distinct. This means the number 1 is not a prime number. Prime numbers have no numbers that go into them equally without a remainder - besides themselves and the number one.  The first five prime numbers should be memorized. They are - 2,3,5,7, and 11. Many SAT math questions will only deal with these first five prime numbers, although this is not always the case.  It should also be noted that the number 2 is a special prime number because it is the smallest prime number. Additionally, it is the only prime number that is even. It it very common for SAT test makers to intentionally make questions dealing with prime numbers tricky. The best defense against this is to read the questions carefully and completely, paying special attention to the exact information that they want. By eliminating one or more choices, it increases your chances of getting a correct answer - and points for the question.  Difference Between Factors and Multiples Basically, a factor is a number that will go into another number with no remainder. For example, the factors of the number 20 are 1, 20, 2, 10, 4, and 5. It is important to pay special attention to the ordering of factors. One should be first, followed by the number itself. By doing it this way, the chances of forgetting a number and leaving it out are lessened quite dramatically.  TIP: It is important to never forget about the number one (1) and the number in the question. Even prime numbers have these as a factor. Some SAT math questions will try to intentionally trick you. Because of this, it is important to pay close attention to the number of factors a number has - including itself and the number one.  On the other hand, prime factors are prime numbers that can be divided into a number without a remainder. On the SAT math section, chances are high that prime factorization will come up. It is a good idea to read these questions carefully to figure out exactly what information they want. Listing prime numbers and prime factorization are different and will give different answers. The chances are high that the wrong answer will be one of the choices on multiple choice sections.  A multiple is a number that is derived from multiplying two integers together. These are commonly referred to as the multiplication tables. For example, multiples of 4 are 8, 12, 16 and so on.  TIP: Multiples are answers gotten when multiplied by an integer. For example, zero, negatives and the number on its own are all considered multiples. Knowing this, SAT test makers often rely on the fact that test takers get factors and multiples confused. They will intentionally give answers that may seem right even though they are incorrect.  Greatest Common Factor / Lowest Common Multiple  In order to find the GCF (greatest common factor) of two numbers, simply write down the factors of each number and choose the largest one, even if it is one of the two original numbers. This is another area where the test makers really try to confuse test takers. Because of this, practicing finding the GCF is recommended for those who want to increase their math SAT scores.  To find the LCM (lowest common multiple) simply use the prime factorization tree, although there is a difference from finding the GCF. When finding the LCM, it is only necessary to keep one of each number. Next, multiply the common numbers by all the prime factors left. This will eventually lead to the correct answer for LCM questions on the math section of the SAT.