Number Theory Calculators
Free LCM, GCF, Fibonacci, and prime number calculators. Solve number theory problems step by step with full working.
Number Theory Calculators - Primes, Factors, and Multiples
Number theory is the branch of mathematics that studies the properties of integers - divisibility, prime numbers, factors, multiples, and the relationships between them. These calculators make number theory accessible: from simplifying fractions using GCF to finding scheduling cycles with LCM.
LCM and GCF Calculator - Calculate the Least Common Multiple and Greatest Common Factor of 2 to 6 numbers simultaneously. Shows prime factorization of each number and step-by-step Euclidean algorithm working for GCF. Essential for simplifying fractions, finding least common denominators, and solving scheduling problems.
Fibonacci Calculator - Find any Fibonacci number F(n) up to F(1000) with exact digit count, check if any number is a Fibonacci number, or generate a sequence between two indices. Shows the golden ratio approximation F(n)/F(nโ1) converging to ฯ โ 1.618.
Digital Root Calculator - Find the digital root of any integer by repeatedly summing its digits until a single digit remains. Shows each summation step, computes additive persistence and digital sum, and supports any base from 2 to 36. Also generates digital root tables for integer ranges.
Number Base Converter - Convert integers and fractions between any two bases from 2 to 36: binary, octal, decimal, hexadecimal, and beyond. Shows binary in nibble groups, displays all four common bases simultaneously, and provides full step-by-step positional expansion and repeated-division working.
Applications of Number Theory
GCF (Greatest Common Factor): Used to simplify fractions (divide numerator and denominator by their GCF), divide items into the largest equal groups, and reduce measurements. Example: 24 apples and 36 oranges can be arranged into GCF(24,36) = 12 identical baskets.
LCM (Least Common Multiple): Used to add fractions with different denominators (find the LCD), schedule repeating events (when will they next coincide?), and solve tiling and packing problems. Example: if bus A runs every 12 minutes and bus B every 18 minutes, they next depart together after LCM(12,18) = 36 minutes.
Frequently Asked Questions
What is the difference between LCM and GCF?
GCF (Greatest Common Factor) is the largest number that divides all given numbers exactly. LCM (Least Common Multiple) is the smallest number that all given numbers divide into exactly. For 12 and 18: GCF = 6, LCM = 36. Relationship: LCM ร GCF = product of the two numbers (for two numbers).
Is GCF the same as GCD or HCF?
Yes - all three terms refer to the same concept. GCF (Greatest Common Factor) is common in US curricula. GCD (Greatest Common Divisor) is used in higher mathematics and computer science. HCF (Highest Common Factor) is used in British and Indian curricula. The calculation and result are identical.
What is the Euclidean Algorithm?
The Euclidean Algorithm is an efficient method for finding the GCF of two numbers by repeatedly dividing and taking remainders until the remainder is 0. The last non-zero remainder is the GCF. It is attributed to the ancient Greek mathematician Euclid (c. 300 BCE) and remains one of the oldest and most efficient algorithms in mathematics.