Prime Factorization Calculator
Find all prime factors, a factor tree, all divisors and divisibility rules for any number
What Is Prime Factorization?
Every integer greater than 1 is either prime (divisible only by 1 and itself) or composite (can be written as a product of primes). Prime factorization is the process of writing a number as a product of its prime factors — the "atomic" building blocks of numbers. This is unique for every number (the Fundamental Theorem of Arithmetic).
The Division Method
Divisibility Rules
÷2: Last digit is even. ÷3: Sum of digits divisible by 3. ÷4: Last two digits divisible by 4. ÷5: Ends in 0 or 5. ÷6: Divisible by both 2 and 3. ÷9: Sum of digits divisible by 9. ÷10: Ends in 0. ÷11: Alternating digit sum divisible by 11.
// Fundamental Theorem
Every integer > 1 has exactly one prime factorization (ignoring order). This is the Fundamental Theorem of Arithmetic.
// Count Factors
If n = p^a × q^b × r^c, the total number of factors is (a+1)(b+1)(c+1). Useful for factorization puzzles.
// Perfect Squares
A number is a perfect square if and only if all exponents in its prime factorization are even. e.g. 36 = 2² × 3² ✓
// Largest Prime Factor
After dividing by all small primes, if the remaining quotient > 1, it is itself prime — the largest prime factor.