Find all factors, factor pairs, and prime factorization of any integer. Instantly shows factor count, sum of factors, and number properties.
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To find all factors of a positive integer n, divide it by every integer from 1 up to the square root of n. If the division is exact, both the divisor and the quotient are factors. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24 — eight factors in total.
A factor (or divisor) of a positive integer is any whole number that divides it without leaving a remainder. Every positive integer has at least two factors: 1 and itself. Numbers with exactly two factors are called prime numbers; numbers with more than two factors are called composite numbers.
Divisibility test
a ∣ n ⇔ n ÷ a = k, where k is an integerFind every factor, factor pair, and prime factorization in one click — no manual trial division required.
Handles integers up to 1,000,000, which would take minutes to factor by hand.
See exactly which divisors were tested and how each factor pair was found — great for learning and homework.
Automatically identifies whether the number is prime, composite, a perfect square, or a perfect cube.
Find common factors of numerator and denominator to reduce a fraction to its simplest form.
The prime factorization of each number is the foundation for computing the greatest common divisor and least common multiple.
Quickly check which numbers evenly divide a given integer — useful in number theory, puzzles, and competition math.
Students use factor lists to practise number sense, prime vs composite classification, and factor tree construction.
A factor of a number is any integer that divides it evenly (with no remainder). For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Test every integer from 1 up to the square root of n. If n is divisible by i, then both i and n/i are factors. This approach avoids checking every number up to n.
Factors divide into a number evenly (12 ÷ 3 = 4, so 3 is a factor of 12). Multiples are the result of multiplying a number (12 × 3 = 36, so 36 is a multiple of 12).
Prime factorization expresses a number as a product of prime numbers. For example, 60 = 2² × 3 × 5. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
A prime number has exactly two factors: 1 and itself. That is the definition of a prime number.
Yes — a number has an odd number of factors if and only if it is a perfect square. For example, 36 has 9 factors because √36 = 6 is a whole number and pairs with itself.