Module · Arithmetic & Number Properties
Chapter 3: Primes & Prime Factorization
Arithmetic
4 topics
What this chapter covers
The 4 topics below make up Primes & Prime Factorization on the GRE. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Primes & factorization
| Prime | exactly two factors: 1 and itself |
|---|---|
| Smallest / only even prime | 2 |
| Fundamental Theorem | unique prime factorization for n > 1 |
| Primality check up to | √n (test primes ≤ √n) |
Counting from exponents
| n = p^a · q^b · r^c | number of factors = (a+1)(b+1)(c+1) |
|---|---|
| Perfect square | every prime exponent is even |
| Perfect cube | every prime exponent is a multiple of 3 |
| Odd number of factors ⇔ | n is a perfect square |
GRE reference
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