Prime Factorization Calculator
Prime factorization of any whole number from 2 to 999,999,999,999, shown as a product and as powers: 360 = 2^3 × 3^2 × 5. How it works
Use the Prime Factorization Calculator
About the Prime Factorization Calculator
360 = 2 × 2 × 2 × 3 × 3 × 5, which is 2^3 × 3^2 × 5. Enter a whole number from 2 to 999,999,999,999 and the calculator lists its prime factors, smallest first, and groups repeats as powers. A prime number comes back as itself, with the note that only 1 and itself divide it. The page also lists the division steps and every divisor: 360 has 24.
Prime factorizations
| Number | Prime factors | As powers |
|---|---|---|
| 12 | 2 × 2 × 3 | 2^2 × 3 |
| 100 | 2 × 2 × 5 × 5 | 2^2 × 5^2 |
| 360 | 2 × 2 × 2 × 3 × 3 × 5 | 2^3 × 3^2 × 5 |
| 1001 | 7 × 11 × 13 | 7 × 11 × 13 |
| 1024 | 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 | 2^10 |
| 2310 | 2 × 3 × 5 × 7 × 11 | 2 × 3 × 5 × 7 × 11 |
| 600851475143 | 71 × 839 × 1471 × 6857 | 71 × 839 × 1471 × 6857 |
| 999999999989 | 999999999989 | 999999999989 |
| 999999999999 | 3 × 3 × 3 × 7 × 11 × 13 × 37 × 101 × 9901 | 3^3 × 7 × 11 × 13 × 37 × 101 × 9901 |
As the tool shows them. 999999999989 is a prime number: the tool shows it as its own single factor and adds a Prime number badge. 999999999999 is the largest number the tool accepts.
How to use this tool
- Type a whole number from 2 to 999,999,999,999 (up to 12 digits). It starts with 360.
- Read the product of primes and the same factors grouped as powers. Open Show the division steps for the chain of divisions, or All divisors for the count and the full list.
- If a message appears, it says why the entry cannot be factored: a decimal, a negative number, an exponent form such as 1e3, or more than 12 digits.
Frequently asked questions
- What is the prime factorization of 360?
- 2 × 2 × 2 × 3 × 3 × 5, or 2^3 × 3^2 × 5. Dividing 360 by 2 three times gives 45, and 45 ÷ 3 ÷ 3 leaves 5, which is prime. 360 has (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors, from 1, 2, 3, 4, 5, 6 up to 180 and 360.
- How do I know if a number is prime?
- If the result is a single factor, the number itself, it is prime. 97 and 1000000007 each come back as themselves, while 1001 is not prime: 7 × 11 × 13. The number 1 is not prime and has no prime factors, so the tool asks for 2 or more.
- How do I find the GCD or LCM from prime factors?
- Write both numbers as prime powers. The GCD takes each shared prime with the smaller exponent, and the LCM takes every prime with the larger exponent. For 360 = 2^3 × 3^2 × 5 and 84 = 2^2 × 3 × 7, the GCD is 2^2 × 3 = 12 and the LCM is 2^3 × 3^2 × 5 × 7 = 2520.
- What is the largest number it can factor?
- 999,999,999,999, which is 12 digits. A 13-digit number gets "Number too large: the limit is 999,999,999,999 (12 digits)." The largest input factors as 3^3 × 7 × 11 × 13 × 37 × 101 × 9901.
- Why does it reject 2.5, -5 or 1e3?
- Prime factors belong to whole numbers greater than 1, so each of these gets a message: decimals have no prime factors, negatives are not factored here, and 1e3 must be typed in full as 1000. To factor -360, factor 360 and put -1 in front: -360 = -1 × 2^3 × 3^2 × 5.
- Can it factor the numbers used in RSA encryption?
- No. RSA relies on the difficulty of factoring the product of two large primes, and its numbers are far longer than 12 digits. No algorithm that runs in polynomial time on a classical computer is known for large integers, though none is proved impossible.
Related Tools
View all toolsQuadratic Equation Solver
Solve ax² + bx + c = 0 for real or complex roots, with the discriminant, vertex, axis of symmetry, step list and a parabola plot.
Matrix Calculator
Add, subtract and multiply matrices up to 10 × 10, or get the determinant, inverse, transpose, rank and row-reduced form. Answers are exact fractions.
LCM and GCD Calculator
GCD (also called GCF or HCF) and LCM of 2 to 10 whole numbers, with the Euclidean steps and the prime factors of each number shown.
Standard Deviation
Standard deviation calculator for a list of numbers: population σ and sample s side by side, both variances, plus mean, median, minimum, maximum, range and sum.
Percentage Calculator
Percentage calculator for seven questions: X% of Y, X is what % of Y, percent change, percent difference, X is Y% of what, and a percent increase or decrease.
Prime Number Checker
Type a whole number below 3.3 × 10^24 to see whether it is prime. A composite gets its smallest prime factor, and the five primes on either side are listed.