A free, self-paced textbook in 7 chapters. Read a chapter, then drill it with the 161 companion flashcards using spaced repetition.
The building blocks of number theory on the GMAT begin with classifying integers. Whole numbers include \(0, 1, 2, 3, \ldots\) while integers extend in both directions: \(\ldots, -...
The fastest divisibility checks on the GMAT rely on digit rules. A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8); by 5 if its last digit is 0 or 5; by 4 if its...
Once an integer is broken into prime factors, several powerful quantities become easy to compute. To count the divisors of a number, write its prime factorization, add 1 to every e...
Modular arithmetic collapses huge numbers into small, manageable remainders. The fundamental distributive property is \((a \cdot b) \bmod n = ((a \bmod n)(b \bmod n)) \bmod n\), wh...
A factorial \(n!\) is the product \(1 \cdot 2 \cdot 3 \cdots n\), with the convention that \(0! = 1\). For reference, \(10! = 3{,}628{,}800\). Factorials connect directly to combin...
Standard sum formulas cover the most common arithmetic series. The sum of the first \(n\) positive integers is \(S_n = \frac{n(n+1)}{2}\), so \(1 + 2 + \cdots + 100 = 5050\). The s...
Percent-to-decimal conversion is a moving-the-point operation: shift the decimal two places left. Thus 12.5% becomes 0.125, and 7% of 250 equals 0.07 × 250 = 17.5. The complementar...