Math
Prime Factorization Calculator (up to 1,000,000)
Instantly factorize any integer N from 2 to 1,000,000 into prime factors. Shows step-by-step division, divisors, divisor count, and divisor sum. Includes 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 | — |
Tips
- 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.
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.