Factor Calculator

Find all factors, prime factors, factor pairs, and analyze number properties with detailed mathematical explanations and classifications.

Factor Analysis

Enter a number to analyze its factors and properties

Number

Enter a positive integer (1 to 1,000,000)

Analysis Focus

Show divisibility rules analysis

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Types of Factors

All Factors

Every positive integer that divides evenly into the number, including 1 and the number itself. Found by testing divisibility from 1 to √n and including corresponding quotients.

Example: Factors of 12 = 1, 2, 3, 4, 6, 12

Proper Factors

All factors except the number itself. Used to classify numbers as perfect, abundant, or deficient based on whether their sum equals, exceeds, or is less than the original number.

Example: Proper factors of 12 = 1, 2, 3, 4, 6 (sum = 16 > 12, so 12 is abundant)

Prime Factors

The prime numbers that multiply together to give the original number. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).

Example: Prime factors of 12 = 2, 3 (since 12 = 2² × 3)

Factor Pairs

Pairs of factors that multiply to give the original number. Useful for understanding the structure of a number and for applications like finding rectangles with given area.

Example: Factor pairs of 12 = (1,12), (2,6), (3,4)