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GRE Math Basics Part 2: Factors, Multiples, and Prime Numbers

  • by John
  • Mar 02, 2014
  • GRE Blog, GRE Tutor

There certainly is a lot to know when preparing for the GRE.  However, it is imperative that you are studying highly tested facts versus ambiguous material that rarely shows up on the test.  It’s easy to think that you simply need to focus on high school math concepts such as geometry, algebra, proportions, fractions, percents, decimals, and the order of operations (PEMDAS ), but it simply isn’t true.  That list is not exhaustive and it is extremely difficult to revisit four years of high school math plus a few university courses in the limited time you have to prepare for the GRE.  So, we made things easier!  Despite the fact that everyone’s exam is distinct, there are commonly tested concepts that will help rack up valuable Test Day points.  These are must know facts that are commonly tested on the GRE.

Here are some must-know math facts that will help you navigate the GRE.

  • A factor of a number is any positive integer that can be multiplies by an integer to equal the number.  For example, the factors of 12 are 1,2,3,4,6,12.
  • A multiple of a number is the product of that number and any other whole number.  For example, some multiples of 12 are 12, 24, 36, 48 …
  • Remember that there are few factors and many multiples.
  • A prime number is a positive integer greater than 1 that is divisible by 1 and itself.

For example:  2, 3, 5, 7, 11 ….

  • The number one is NOT prime.
  • The number two is the only even prime number.
  • The number two is the smallest prime number.
  • Zero is not prime.
  • Negative numbers are not prime.
  • Every positive, nonprime number greater than 1 can be expresses as the product of a series of prime numbers.

Common GRE percent conversions

You are permitted to use a calculator on the GRE.  However, knowing common percents, decimal and fractions conversions can save a lot of time.  It is very helpful on Test Day to be able to convert fractions to decimals and percents and vice versa.  Here is a chart with commonly used percents:

5%                   .05       1/20

10%                 .1         1/10

12.5%              .125     1/8

16 2/3%           .167     1/6

20%                 .2         1/5

25%                 .25       ¼

30%                 .3         3/10

33 1/3%           .33       1/3

50%                 .5         1/2

 GRE Ratios

The GRE can describe ratios in various forms.  For example, the ratio of X to Y can be written as X/Y or X:Y.  If you are given a ratio and an actual number of items that corresponds to one of the components of the ratio, you can determine the number of items represented by each of the other components of the ratio.  Consider the problem below:


      Column A                                                              Column B


The ratio of boys to girls in a classroom

is 2:5 and there are 35 girls in the class.


The # of boys in the class                                               14


First translate boys and girls into a fraction and plug in the numbers.  So boys/girls = 2/5.  Then plug in the variable over the total amount of girls and set the two fractions equal to each other.  So:   2/5 = B/35. Then cross multiply to get (5B) = 70, so B = 14.  These columns are equal so the correct answer is (C).

Join us next time for GRE triangle basics. 

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