GRE Quant: Prime and Non-Prime Numbers

Prime and non-prime numbers form a key theme in GRE Quant questions, and a clear understanding of how these numbers behave creates a strong base for solving many Quant problems. Straightforward definitions lead to layered outcomes, and steady familiarity with prime structure helps you spot patterns, evaluate factor behavior, and reason accurately across a wide range of GRE Quant questions.

The following video, part of the GRE preparation course by Experts’ Global, explains prime and non-prime numbers in a clear, structured, and intuitive manner. It walks you through how primes and non-primes behave within expressions, products, and conditions, and highlights patterns that frequently shape answer choices on GRE Quant questions. Take your time to absorb this topic and apply the learnings steadily across your GRE practice drills, GRE sectional mock tests, and GRE full mock tests.

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Overview: Prime and Non-Prime Numbers

Prime and non-prime numbers on GRE Quant

Prime Numbers

Prime numbers are integers that have exactly 2 factors. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.

Composite Numbers

Integers with more than 2 factors are referred to as composite numbers. It is important to note that the specific term “composite” is not tested on the GRE.

GRE Terminology

Because the term “composite” is not used, the GRE categorizes integers using the following two terms:

Prime numbers
Non-prime numbers

Primality Check

Checking whether an integer is prime on GRE Quant

To check whether an integer x is prime, you do not need to check for divisibility by all integers between 2 and x, nor do you need to check all prime numbers between 2 and x.

You only need to check for divisibility by all prime numbers less than the square root of x.

Examples

1. Is 23 a prime number?

To determine this, check for divisibility only by prime numbers less than the square root of 23.
The square root of 23 is between 4 and 5.
The primes to check are: 2 and 3.
Since 23 is not divisible by 2 and 3, it is a prime number.

2. Is 47 a prime number?

To determine this, check for divisibility only by prime numbers less than the square root of 47.
The square root of 47 is between 6 and 7.
The primes to check are: 2, 3, and 5.
Since 47 is not divisible by 2, 3, and 5, it is a prime number.

Practice Set: Primality Check

A conceptual exercise on GRE Quant

Answer: 2, 3, 11, 23, 31, 43, 59, 67, 79 are prime

For a detailed explanation, please refer to the video presented earlier on this page.

Question

Which of the following integers are prime numbers?

Explanation

To determine if an integer “x” is prime, you only need to check for divisibility by all prime numbers less than the square root of x. If none of these primes divide x evenly, then x is prime.

Here is the evaluation of the list based on this methodology:

1: Not prime by definition (a prime number must have exactly two factors; 1 has only one factor).
2: Prime (the smallest and only even prime number).
3: Prime.
4: Not prime (divisible by 2; factors are 1, 2, 4).
11: Prime (√11 is between 3 and 4; not divisible by 2 or 3).
15: Not prime (divisible by 3 and 5).
22: Not prime (divisible by 2 and 11).
23: Prime (√23 is between 4 and 5; not divisible by 2 or 3).
27: Not prime (divisible by 3).
31: Prime (√31 is between 5 and 6; not divisible by 2, 3, or 5).
39: Not prime (divisible by 3; 3 × 13 = 39).
43: Prime (√43 is between 6 and 7; not divisible by 2, 3, or 5).
51: Not prime (divisible by 3; 3 × 17 = 51).
59: Prime (√59 is between 7 and 8; not divisible by 2, 3, 5, or 7).
67: Prime (√67 is between 8 and 9; not divisible by 2, 3, 5, or 7).
79: Prime (√79 is between 8 and 9; not divisible by 2, 3, 5, or 7).