The Factor Calculator finds all factors of a number, its prime factorisation, and factor pairs. It can also compute the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of two numbers.
Enter any positive integer to see its complete factorisation. The calculator uses trial division for efficient computation and displays results clearly.
Your calculations will appear here
A factor (or divisor) of a positive integer n is any positive integer that divides n without leaving a remainder. Every positive integer has at least two factors: 1 and itself. Numbers with exactly two factors are called prime numbers, while numbers with more than two factors are called composite numbers.
Prime factorisation expresses a composite number as a product of prime numbers. By the Fundamental Theorem of Arithmetic, every integer greater than 1 has a unique prime factorisation (up to the order of the factors). This decomposition is the foundation for many results in number theory.
The Greatest Common Divisor (GCD) of two integers is the largest positive integer that divides both numbers. The Euclidean algorithm computes it efficiently by repeatedly replacing the larger number with the remainder of dividing the two, until the remainder is zero. The last non-zero remainder is the GCD.
The Least Common Multiple (LCM) of two integers is the smallest positive integer divisible by both. It is related to the GCD by the identity LCM(a, b) = (a * b) / GCD(a, b). This relationship makes computing the LCM straightforward once the GCD is known.
Problema: List every positive integer that divides 36.
Solucion: Test integers from 1 to sqrt(36) = 6. 36 / 1 = 36, 36 / 2 = 18, 36 / 3 = 12, 36 / 4 = 9, 36 / 6 = 6. Collect both divisor and quotient.
Respuesta: 1, 2, 3, 4, 6, 9, 12, 18, 36
Problema: Express 180 as a product of prime factors.
Solucion: 180 / 2 = 90, 90 / 2 = 45, 45 / 3 = 15, 15 / 3 = 5, 5 is prime.
Respuesta: 2^2 * 3^2 * 5
Problema: Find all pairs (a, b) where a * b = 24.
Solucion: Test from 1 upward: 1 * 24, 2 * 12, 3 * 8, 4 * 6. Stop when a > sqrt(24).
Respuesta: (1, 24), (2, 12), (3, 8), (4, 6)
Problema: Find the greatest common divisor of 48 and 36 using the Euclidean algorithm.
Solucion: gcd(48, 36): 48 / 36 = 1 remainder 12. gcd(36, 12): 36 / 12 = 3 remainder 0. The last non-zero remainder is 12.
Respuesta: 12
Problema: Find the least common multiple of 15 and 20.
Solucion: First find GCD(15, 20) = 5. Then LCM = (15 * 20) / 5 = 300 / 5.
Respuesta: 60
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