Find all factors, prime factors, factor pairs, and complete prime factorization with step-by-step visualization.
A factor (or divisor) of a number is an integer that divides that number evenly without leaving a remainder. For example, factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 evenly.
Prime factors are the prime numbers that multiply together to give the original number. For example, the prime factors of 12 are 2 and 3 because 2 × 2 × 3 = 12. Every integer has a unique prime factorization.
Prime factorization is expressing a number as a product of prime numbers. It's unique for each number (Fundamental Theorem of Arithmetic). For example, 24 = 2³ × 3. This is useful in simplifying fractions and finding GCF/LCM.
To find factors manually: test each integer from 1 up to the square root of the number. If the number divides evenly, both the divisor and quotient are factors. List all factors in ascending order.
A perfect number equals the sum of its proper factors (excluding itself). For example, 6 is perfect because 1 + 2 + 3 = 6. Other perfect numbers include 28, 496, and 8128.
