In this module, you'll learn all of the concepts, techniques and strategies needed to answer integer properties questions on the GRE. In particular, this module covers:

  • Divisors and divisibility
  • Primes
  • Squares of integers
  • Rules of divisors
  • Odd/even numbers
  • Testing cases
  • Greatest common divisor (GCD)
  • Least common multiple (LCM)
  • The GCD-LCM formula
  • Properties of consecutive integers
  • Remainders

Two ways to prepare

Beneath most of the video lessons below, you’ll find a Reinforcement Activities box containing practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on remainders). With this lesson format, you have two study options:

  • Watch the video lesson first and then reinforce your learning by answering several related questions, or…
  • Tackle the practice questions first and watch the lesson only if you need help with the concepts the practice questions test

For more on this learning strategy, read the “How to Beat the GRE” section of our course overview page.

GRE INTEGER PROPERTIES VIDEOS

  • 1. Lesson: Introduction to Divisibility (6:12)
  • 2. Question: Number of Divisors (1:21)
  • 3. Lesson: Divisibility Rules (7:03)
  • 4. Lesson: Prime Numbers (1:49)
  • 5. Question: Number of Primes (1:51)
  • 6. Lesson: Prime Factorization (7:45)
  • 7. Question: Prime Divisors (2:07)
  • 8. Question: Greatest Integer n (2:02)
  • 9. Lesson: Counting the Divisors of Large Numbers (5:08)
  • 10. Lesson: Squares of Integers (4:01)
  • 11. Question: 2520k is a Perfect Square (1:55)
  • 12. Lesson: Divisor Rules (5:26)
  • 13. Lesson: Greatest Common Divisor (GCD) (6:13)
  • 14. Question: GCD of x and y is 12 (3:00)
  • 15. Lesson: Least Common Multiple (LCM) (4:58)
  • 16. Lesson: The GCD-LCM Formula (2:07)
  • 17. Lesson: Even and Odd Integers (9:09)
  • 18. Lesson: Testing Possible Cases (5:28)
  • 19. Question: What Must Be True? (1:44)
  • 20. Lesson: Consecutive Integers (4:59)
  • 21. Lesson: Introduction to Remainders (6:45)
  • 22. Question: Quotient is x (3:56)
  • 23. Question: Not divisible by 6 (5:10)
  • 24. Lesson: Integer Properties Strategies (3:58)
  • 25. Question: w and k are Integers (2:44)
  • 26. Question: Least Common Multiple is 168 (1:17)
  • 27. Question: 12 is a divisor of n (2:43)
  • 28. Question: Also Prime (1:35)
  • 29. Question: K Divided by 67 (4:48)
  • 30. Question: Consecutive Integers p, q, r and s (2:15)
  • 31. Question: 2N Divided by D (3:39)
  • 32. Question: Divisible by 3 (2:48)
  • 33. Question: Divisor of 86,420 (2:47)
  • 34. Question: Remainder when Divided by 7 (3:32)
Total viewing time for the GRE Integer Properties module: 132 minutes.

Practice from the Official Guide

Practice the skills and GRE-specific strategies you learned in this module by answering the following questions from the Official Guide to the GRE (3rd edition):

  • 115(1), 126(2), 169(14), 232(3-7), 233(14-15)

 

Here are the related questions in the Official Guide to the GRE (1st or 2nd edition):

  • 110(1), 121(2), 159(14) 

 

Note: The above practice questions are listed in the form page#(question#). So, for example, 110(1) represents question #1 on page 110.

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