Number Theory is a branch of mathematics focused on properties of integers. In coding interviews, it appears in problems involving divisibility, prime numbers, modular arithmetic, greatest common divisor (GCD), and least common multiple (LCM). Mastering number theory helps you design efficient solutions for problems that would otherwise be too slow with brute force.
Many interview problems rely on mathematical insights rather than complex data structures. Recognizing patterns such as modular cycles, prime factorization, or gcd relationships can drastically reduce time complexity. These ideas frequently combine with other DSA concepts like Math, Bit Manipulation, and Combinatorics to build optimized solutions.
While practicing Number Theory problems, you will commonly encounter techniques such as:
On TalentD's DSA Corner, these 63 curated Number Theory practice questions are designed to help you recognize mathematical patterns quickly and apply them effectively in real coding interviews.
Provides the mathematical foundation needed for concepts like divisibility, modular arithmetic, and prime numbers.
Often used to store remainders, factors, or computed results when solving number-based problems efficiently.
Useful for solving counting problems that rely on mathematical formulas and number properties.
Helps optimize numeric computations and appears in problems involving powers, parity, and binary properties.
| Status | Title | Video | Leetcode | Solve | Difficulty | Companies | Topics |
|---|---|---|---|---|---|---|---|
| 258. Add Digits | Solve | Easy | Bloomberg | ||||
| 914. X of a Kind in a Deck of Cards | Solve | Easy | Google | ||||
| 1952. Three Divisors | Solve | Easy | Microsoft | ||||
| 1979. Find Greatest Common Divisor of Array | Solve | Easy | TIAA | ||||
| 2413. Smallest Even Multiple | Solve | Easy | Adobe+2 | ||||
| 2427. Number of Common Factors | Solve | Easy | - | ||||
| 2614. Prime In Diagonal | Solve | Easy | - | ||||
| 2748. Number of Beautiful Pairs | Solve | Easy | - |
Start Easy, progress to Hard.
Frequently appear alongside Number Theory.
Common questions about Number Theory.
Yes. Many interview problems involve modular arithmetic, prime numbers, or mathematical observations that reduce time complexity. Strong number theory knowledge helps you solve such problems quickly.
Number Theory in DSA focuses on mathematical properties of integers such as primes, divisibility, modular arithmetic, and gcd/lcm. These concepts help solve optimization and arithmetic-heavy coding problems efficiently.
Companies like Google, Amazon, Microsoft, and competitive programming platforms frequently include number theory problems, especially those involving primes, modular math, and mathematical optimizations.
Practicing 40–60 well-chosen problems is usually enough to understand common patterns. The 63 problems in this section provide solid coverage of key interview concepts.
Popular techniques include the Euclidean algorithm for GCD, the Sieve of Eratosthenes for generating primes, modular exponentiation, and prime factorization methods.