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

 Divisibility and divisors Prime numbers 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 each video lesson in this module, we have a Related Resource box with practice questions that test the concepts covered in the video. With this lesson format, you have two learning 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

## GMAT INTEGER PROPERTIES VIDEOS

• 1. Lesson: Introduction to Divisibility (6:35)
• 2. Question: Number of Divisors (1:21)
• 3. Lesson: Divisibility Rules (7:03)
• 4. Question: N=5314+k (3:28)
• 5. Lesson: Prime Numbers (1:49)
• 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. Question: 6 a divisor of x (3:18)
• 14. Lesson: Greatest Common Divisor (GCD) (6:13)
• 15. Question: GCD of x and y is 12 (3:00)
• 16. Lesson: Least Common Multiple (LCM) (4:58)
• 17. Lesson: The GCD-LCM Formula (2:07)
• 18. Lesson: Even and Odd Integers (9:09)
• 19. Question: Is x Even (2:43)
• 20. Lesson: Testing Possible Cases (5:44)
• 21. Question: What Must Be True? (1:44)
• 22. Lesson: Consecutive Integers (4:59)
• 23. Lesson: Introduction to Remainders (6:45)
• 24. Question: Quotient is x (3:56)
• 25. Question: Not divisible by 6 (5:10)
• 26. Lesson: Integer Properties Strategies (4:01)
• 27. Question: w and k are Integers (2:44)
• 28. Question: Is n Even? (1:45)
• 29. Question: GCD of x and y (3:08)
• 30. Question: 12 is a divisor of n (2:43)
• 31. Question: Are w, x and y Consecutive? (2:24)
• 32. Question: K Divided by 67 (4:48)
• 33. Question: Is k Divisible by 18? (3:28)
• 34. Question: 2N Divided by D (3:39)
• 35. Question: Divisible by 3 (2:48)
• 36. Question: Divisor of 86420 (2:47)
• 37. Question: Remainder when Divided by 7 (3:32)
• 38. Question: GCD of J and K (5:17)
Total viewing time for the GMAT Integer Properties module: 152 minutes.

NOTE: In each of the above video lessons, you’ll find a Related Resources box containing several practice questions that are specifically related to the concepts covered in that lesson (e.g., the lesson on remainders). Conversely, the practice questions below cover a variety of topics under the umbrella of GMAT Integer Properties, and are intended for general reinforcement.

Given this, you may find it beneficial to work on the questions below after you’ve mastered the module content by watching the video lessons and answering concept-specific practice questions from the Related Resources boxes. For more on this learning strategy, visit our course overview page.

Problem Solving (level of difficulty: 350 to 500)

Rhyming primes (prime numbers)

Prime factors (prime factorization)

Product wxyz (prime factorization)

Even and odd m-values (integer properties, strange operators)

Problem Solving (level of difficulty: 500 to 650)

NOT a divisor of x (divisibility, algebra)

Must be divisor of n  (divisibility, remainders)

Multiple of 990 (divisibility)

GCD of 35x and 20y (divisibility)

Prime factors (divisibility)

Number of zeros (prime factorization)

Bag of chips (prime factorization)

Problem Solving (level of difficulty: 650 to 800)

Possible values of 2x + y (remainders)

Smallest value of x+y+z (remainders)

x is a factor of 2y (divisibility)

From 10! to 10! + 20 (divisibility)

Data Sufficiency (level of difficulty: 350 to 500)

Looking for an even product (integer properties)

Checking whether b is negative  (divisibility, powers)

Is 4 + n/6 an integer? (divisibility)

Find the value of r (remainders)

Data Sufficiency (level of difficulty: 500 to 650)

Is x a multiple of y? (divisibility)

Looking for an integer (divisibility)

Is z even? (divisibility)

When k is divided by 10  (divisibility)

Find value of K (divisibility)

Value of xy (divisibility)

Is N odd? (integer properties, divisibility)

Is n divisible by 6? (divisibility)

Looking for a prime (divisibility)

Data Sufficiency (level of difficulty: 650 to 800)

Product divisible by 8  (divisibility, probability)

Integer root (integer properties, roots)

Value of positive integer m (divisibility, remainders)

GCD of m and n (divisibility)

Multiple of 18 (divisibility)

Is y prime? (divisibility)

## Practice from the Official Guides

Official Guide for GMAT Review (2017 edition)

Problem Solving: 40, 42, 48, 54, 62, 105, 108, 119, 122, 134, 149, 158, 159, 161, 168, 190, 200, 225

Data Sufficiency: 266, 270, 275, 300, 304, 314, 315, 343, 346, 347, 365, 369, 389

Official Guide for GMAT Review (2016 edition)

Problem Solving: 35, 38, 43, 48, 93, 96, 106, 108, 118, 132, 140, 141, 143, 151, 177, 190, 209, 222, 223

Data Sufficiency: 3, 9, 31, 36, 60, 72, 99, 102, 121, 125, 149, 174

Official Guide for GMAT Review (2015/13th edition)

Problem Solving: 5, 26, 40, 44, 74, 77, 87, 95, 110, 116, 117, 118, 127, 155, 174, 204, 218, 219, 221, 225

Data Sufficiency: 7, 14, 27, 32, 58, 72, 80, 83, 111, 135, 173

While answering practice questions from the Official Guide for GMAT Review (2017, 2016 or 2015), you can enter your responses directly into our downloadable Improvement Chart. This will help track your progress and identify areas of weakness.