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Find All Factors & Factor Pairs
Find all factors of any number, see factor pairs, count total factors, and view prime factorization with factor tree visualization and step-by-step solutions.
Enter a positive integer
Enter a number to find its factors
Type any positive integer into the input field. The calculator works with numbers up to 1,000,000.
Click "Find Factors" to see all factors, factor pairs, prime factorization, and whether your number is prime or composite.
Review the complete list of factors, see how they pair up, and understand the prime factorization in both exponential and expanded forms.
A factor is a number that divides evenly into another number with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
Prime numbers have exactly 2 factors (1 and itself). Composite numbers have more than 2 factors. The number 1 is neither prime nor composite.
Factor pairs are two factors that multiply to give the original number. Every number has at least one factor pair: 1 and itself.
Factors divide into a number evenly, while multiples are the result of multiplying a number by integers. For example, factors of 12 are 1, 2, 3, 4, 6, 12 (they divide into 12), while multiples of 12 are 12, 24, 36, 48... (results of multiplying 12 by 1, 2, 3, 4...).
A prime number has exactly 2 factors: 1 and itself. This is the definition of a prime number. For example, 7 is prime because its only factors are 1 and 7. If a number has more than 2 factors, it's called composite.
There's no 'most factors' - larger numbers can have more and more factors. However, highly composite numbers have more factors than any smaller number. For example, 120 has 16 factors, making it highly composite. Numbers with many small prime factors tend to have more total factors.
Yes, but we typically only consider positive factors for simplicity. Every positive factor has a corresponding negative factor. For example, if 3 is a factor of 12, then -3 is also technically a factor since -3 × -4 = 12.
Prime factorization is fundamental in mathematics. It's used to find GCF and LCM, simplify fractions, solve divisibility problems, in cryptography (RSA encryption), and to understand the structure of numbers. Every composite number has a unique prime factorization.
Test divisibility only up to the square root of the number. If a number n = a × b and a ≤ b, then a ≤ √n. So you only need to test factors up to √n, and for each factor found, you automatically get its pair. For 100, test only up to 10.
Factors are the building blocks of numbers in mathematics. A factor of a number is any integer that divides evenly into that number without leaving a remainder. Understanding factors is essential for working with fractions, finding common denominators, and solving many types of mathematical problems.