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Master mathematical algorithms for FAANG DSA interviews: primes, GCD, modular arithmetic, fast exponentiation, combinatorics, and number theory with complexity reference and full problem index.
LC 204 Count Primes is the gateway sieve problem at Google and Amazon. Master the Sieve of Eratosthenes, understand why you start marking at p*p, and apply the technique to interval queries, prime factorization, and every sieve variant an interviewer can ask.
LC 1979 Find Greatest Common Divisor of Array is the entry point to GCD problems at Google and Meta. Master the Euclidean algorithm in O(log n), compute LCM without overflow, and apply extended GCD for modular inverse.
Modular arithmetic powers nearly every competitive programming problem and is foundational at Google, Stripe, and any system that handles big numbers. Master binary exponentiation in O(log n), modular inverse via Fermat little theorem, and the modulo identities that prevent overflow on the hot path.
Prime factorization is the workhorse of number-theoretic interview problems at Amazon and Microsoft. Master trial division in O(sqrt n), the smallest-prime-factor sieve for batched factorization in O(log n) per query, and the divisor-counting tricks they unlock.