Prime Factorization Calculator & Tool — Free Online Site (up to 1,000,000)
Free online prime factorization calculator and tool. Enter any integer up to 1,000,000, even a specific number like 12,825, to see the factor tree, divisor list, count, and sum, plus a 1–100 reference table.
Prime factorization table: 1–100
Reference table showing the prime factorization of every integer from 1 to 100. Primes are highlighted in green.
| N | Factorization | Prime? |
|---|---|---|
| 1 | 1 | — |
| 2 | 2 | Prime |
| 3 | 3 | Prime |
| 4 | 2² | — |
| 5 | 5 | Prime |
| 6 | 2 × 3 | — |
| 7 | 7 | Prime |
| 8 | 2³ | — |
| 9 | 3² | — |
| 10 | 2 × 5 | — |
| 11 | 11 | Prime |
| 12 | 2² × 3 | — |
| 13 | 13 | Prime |
| 14 | 2 × 7 | — |
| 15 | 3 × 5 | — |
| 16 | 2⁴ | — |
| 17 | 17 | Prime |
| 18 | 2 × 3² | — |
| 19 | 19 | Prime |
| 20 | 2² × 5 | — |
| 21 | 3 × 7 | — |
| 22 | 2 × 11 | — |
| 23 | 23 | Prime |
| 24 | 2³ × 3 | — |
| 25 | 5² | — |
| 26 | 2 × 13 | — |
| 27 | 3³ | — |
| 28 | 2² × 7 | — |
| 29 | 29 | Prime |
| 30 | 2 × 3 × 5 | — |
| 31 | 31 | Prime |
| 32 | 2⁵ | — |
| 33 | 3 × 11 | — |
| 34 | 2 × 17 | — |
| 35 | 5 × 7 | — |
| 36 | 2² × 3² | — |
| 37 | 37 | Prime |
| 38 | 2 × 19 | — |
| 39 | 3 × 13 | — |
| 40 | 2³ × 5 | — |
| 41 | 41 | Prime |
| 42 | 2 × 3 × 7 | — |
| 43 | 43 | Prime |
| 44 | 2² × 11 | — |
| 45 | 3² × 5 | — |
| 46 | 2 × 23 | — |
| 47 | 47 | Prime |
| 48 | 2⁴ × 3 | — |
| 49 | 7² | — |
| 50 | 2 × 5² | — |
| 51 | 3 × 17 | — |
| 52 | 2² × 13 | — |
| 53 | 53 | Prime |
| 54 | 2 × 3³ | — |
| 55 | 5 × 11 | — |
| 56 | 2³ × 7 | — |
| 57 | 3 × 19 | — |
| 58 | 2 × 29 | — |
| 59 | 59 | Prime |
| 60 | 2² × 3 × 5 | — |
| 61 | 61 | Prime |
| 62 | 2 × 31 | — |
| 63 | 3² × 7 | — |
| 64 | 2⁶ | — |
| 65 | 5 × 13 | — |
| 66 | 2 × 3 × 11 | — |
| 67 | 67 | Prime |
| 68 | 2² × 17 | — |
| 69 | 3 × 23 | — |
| 70 | 2 × 5 × 7 | — |
| 71 | 71 | Prime |
| 72 | 2³ × 3² | — |
| 73 | 73 | Prime |
| 74 | 2 × 37 | — |
| 75 | 3 × 5² | — |
| 76 | 2² × 19 | — |
| 77 | 7 × 11 | — |
| 78 | 2 × 3 × 13 | — |
| 79 | 79 | Prime |
| 80 | 2⁴ × 5 | — |
| 81 | 3⁴ | — |
| 82 | 2 × 41 | — |
| 83 | 83 | Prime |
| 84 | 2² × 3 × 7 | — |
| 85 | 5 × 17 | — |
| 86 | 2 × 43 | — |
| 87 | 3 × 29 | — |
| 88 | 2³ × 11 | — |
| 89 | 89 | Prime |
| 90 | 2 × 3² × 5 | — |
| 91 | 7 × 13 | — |
| 92 | 2² × 23 | — |
| 93 | 3 × 31 | — |
| 94 | 2 × 47 | — |
| 95 | 5 × 19 | — |
| 96 | 2⁵ × 3 | — |
| 97 | 97 | Prime |
| 98 | 2 × 7² | — |
| 99 | 3² × 11 | — |
| 100 | 2² × 5² | — |
What Is Prime Factorisation?
Prime factorisation is the operation of breaking an integer of 2 or more into a product of primes alone. Enter any integer from 1 to 1,000,000 and this tool works out the steps of the decomposition, the full list of divisors, and the count and sum of those divisors automatically. Even large numbers that would take a while by hand are decomposed instantly.
The result is obtained by trial division, and the intermediate steps are shown too, so it also serves for checking mental arithmetic or work done on paper. It suits a wide range of situations — maths homework, verifying answers in a test, and studying cryptography among them.
How to Use the Prime Factorisation Calculator
- Enter an integer N Type an integer of at least 2 and at most 1,000,000 into the input box.
- Check the decomposition The product of prime factors is shown, along with the intermediate steps of the decomposition.
- Check the divisor information The list of divisors, their count and their sum are all calculated automatically.
- Look up other numbers in the quick table The quick table from 1 to 100 lets you see the prime factorisation of other integers at a glance.
Tips for getting more out of it
- Prime factorization means expressing N as a product of prime numbers. Example: 360 = 2³ × 3² × 5. The Fundamental Theorem of Arithmetic guarantees this representation is unique (up to order).
- The number of divisors follows directly from the factorization. If N = p₁^e₁ × p₂^e₂ × …, the divisor count is (e₁+1)(e₂+1)… Example: 12 = 2² × 3 → (2+1)(1+1) = 6 divisors.
- The sum of divisors is σ(N) = (1+p₁+…+p₁^e₁)(1+p₂+…+p₂^e₂)… Example: 12 → (1+2+4)(1+3) = 7 × 4 = 28.
- The simplest factorization algorithm is trial division: divide by every integer from 2 up to √N. For N ≤ 1,000,000 this requires at most 1000 divisions — fast enough for real-time use.
When Prime Factorisation Comes in Handy
Maths homework and exam preparation
Use it to check your answers and you will spot an arithmetic slip in the intermediate working straight away.
Understanding GCD and LCM
Factorise several numbers and compare them, and how the greatest common divisor and least common multiple arise becomes visible.
Confirming that a fraction is fully reduced
Factorise the numerator and denominator separately, find the primes they share, and confirm you have reduced correctly.
Studying cryptography
When learning about techniques such as RSA that rest on the difficulty of factorisation, working through decompositions by hand gives you a feel for the problem.
Prime Factorisation Glossary
- Prime Number
- An integer of 2 or more with no divisors other than 1 and itself. They run 2, 3, 5, 7, 11 … and there are infinitely many.
- Prime Factor
- A prime that divides a given integer exactly. The prime factors of 12, for instance, are 2 and 3.
- Composite Number
- An integer of 2 or more that is not prime. It can be expressed as a product of two or more primes.
- Exponent
- The number stating how many times the same prime factor is multiplied. In 360 = 2³ × 3² × 5, the exponent of 2 is 3.
- Fundamental Theorem of Arithmetic
- The theorem that every integer greater than 1 has a prime factorisation that is unique up to order.
FAQ
Side Note — RSA encryption and the hardness of factorization
RSA encryption — which secures HTTPS, email, and digital signatures — is built on the asymmetry between multiplication and factorization. Multiplying two large primes together (e.g. each ~1024 bits) takes milliseconds; factoring the resulting product back into those two primes is computationally infeasible with current technology.
A 2048-bit RSA modulus would take longer than the age of the universe to factor with the best-known classical algorithms. This "easy to multiply, hard to factor" asymmetry is the mathematical heart of public-key cryptography. Quantum computers (Shor's algorithm) would break RSA, which is why post-quantum cryptography is an active research area.