What Is Prime numbers on the GMAT?
Prime numbers are integers greater than 1 that have exactly two distinct positive divisors: 1 and themselves. They are the building blocks of all integers and appear frequently in GMAT Quant, especially in number-property questions, divisibility, and least common multiples.
Definition
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In other words, it cannot be formed by multiplying two smaller natural numbers. The first few primes are 2, 3, 5, 7, 11, and 13.
Note that 1 is not prime, and 2 is the only even prime.
Why it matters on the GMAT
Prime numbers are central to many GMAT Quant problems. You'll encounter them in:
- Number properties questions
- Divisibility and remainders
- Least common multiple (LCM) and greatest common factor (GCF)
- Exponents and roots
- Data sufficiency problems
Understanding primes helps you break down large numbers and solve problems efficiently.
A concrete example
Consider the number 30. Its prime factorization is 2 × 3 × 5. This tells us that 30 is divisible by 2, 3, and 5, and that any factor of 30 must be a product of these primes (with exponents 0 or 1).
On the GMAT, you might be asked: "How many distinct prime factors does 30 have?" The answer is 3 (2, 3, and 5).
Common mistakes
- Thinking 1 is prime. It is not.
- Forgetting that 2 is the only even prime.
- Confusing 'prime factors' with 'factors' – prime factors are only the primes in the factorization.
- Not using prime factorization when finding LCM or GCF, leading to errors.
How to practice it
Practice by:
- Listing primes up to 100.
- Factoring numbers into primes quickly.
- Solving GMAT-style number-property problems from official guides.
- Using prime factorization to find LCM and GCF of pairs of numbers.
For more in-depth review, visit our Number Properties page.