Number theory calculators

32 free number theory calculators with step-by-step solutions.

• Is it prime?— Check if any number is prime with divisibility proof
• Next prime— Find the next prime after any number
• Previous prime— Find the largest prime before any number
• Nth prime— Find the 100th, 1000th, or any nth prime
• Primes in range— List all primes between two numbers
• Twin primes— Find all twin prime pairs up to any number
• Goldbach conjecture— Express even numbers as sum of two primes

• Prime factorization— Break numbers into prime factors with factor tree
• GCF & LCM— Greatest common factor and least common multiple
• All factors— List every divisor of a number with factor pairs
• Factor count— Count total number of divisors using prime factorization
• Factor sum σ(n)— Sum of all divisors — determines perfect/abundant/deficient
• Coprime checker— Check if two numbers share no common factor

• Number properties— Complete analysis: parity, primality, divisors, digit sum
• Even/odd checker— Check if a number is even or odd
• Perfect number— Equals sum of its proper divisors (6, 28, 496...)
• Abundant number— Proper divisors sum to more than the number
• Deficient number— Proper divisors sum to less than the number
• Perfect square— Check if n = k² for some integer k
• Perfect cube— Check if n = k³ for some integer k
• Palindrome— Reads the same forwards and backwards
• Is it Fibonacci?— Check if a number belongs to the Fibonacci sequence

• Fibonacci calculator— Find the nth Fibonacci number
• Euler's totient φ(n)— Count integers coprime to n
• Collatz conjecture— Trace the 3n+1 sequence for any starting number
• Multiples generator— Generate the first n multiples of any number
• Modular exponentiation— Calculate a^b mod m efficiently

• Digit sum— Sum all digits of a number, find digital root
• Digit product— Multiply all digits together
• Digit count— Count the number of digits
• Reverse number— Reverse all digits: 12345 → 54321
• Number theory tools— General number theory operations