Prime Factorization Calculator

Find the complete prime factorization of any number. Shows all divisors, a factor tree, and identifies if the number is prime.

⚡ Quick Calculator Get a fast estimate

Enter a Number

360

2^3 × 3^2 × 5

Prime factors

2 × 2 × 2 × 3 × 3 × 5

Unique prime factors

2, 3, 5

Number of prime factors

Number of divisors

All Divisors (24)

1234568910121518202430364045607290120180360

Highlighted in colour = prime divisors

Factor Tree

360
├── 2 (prime)
└──   180
  ├── 2 (prime)
  └──     90
    ├── 2 (prime)
    └──       45
      ├── 3 (prime)
      └──         15
        ├── 3 (prime)
        └── 5 (prime)

How to Use

Enter any positive integer. The calculator shows its prime factorization in exponential notation, lists all divisors, and draws a factor tree for numbers up to 10,000.

The Extended Calculator adds an interactive factor tree SVG, prime range finder (Sieve), and a divisor table. The Professional Calculator includes the Sieve of Eratosthenes visualization, prime counting function π(x) chart, and twin prime tables.

Need more detail?

📊 Extended Calculator More options, charts, and scenario comparison

Number to factorize

Prime Factorization of 360

2^3 × 3^2 × 5

All prime factors

2 × 2 × 2 × 3 × 3 × 5

Number of divisors

Sum of divisors

1170

Is prime?

Factor Tree

Blue circles = prime factors

All Divisors (24)

1234568910121518202430364045607290120180360

Prime Factorization Method

Trial division: Divide by 2, then 3, then 5, 7, 11... until you reach √n.

Result format: n = p₁^a₁ × p₂^a₂ × p₃^a₃ × ...

Number of divisors: (a₁+1)(a₂+1)(a₃+1)...

Fundamental Theorem: Every integer > 1 has a unique prime factorization.

Worked Example

Factorize 360:

360 ÷ 2 = 180; ÷ 2 = 90; ÷ 2 = 45; ÷ 3 = 15; ÷ 3 = 5

360 = 2³ × 3² × 5

Divisors: (3+1)(2+1)(1+1) = 24 divisors

Is 97 prime? √97 ≈ 9.8; test 2,3,5,7 — none divide → Prime

Need full precision?

🔬 Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown

Limit (max 200)

Step (show elimination for prime 2)

Primes up to 100

Largest prime

Currently eliminating

Multiples of 2

23456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100

Blue= primeYellow= being eliminated nowRed= composite

Frequently Asked Questions

A prime number is a whole number greater than 1 with exactly two divisors: 1 and itself. The first primes are 2, 3, 5, 7, 11, 13... Note that 2 is the only even prime; 1 is neither prime nor composite.

The Fundamental Theorem of Arithmetic: every integer greater than 1 can be written as a product of prime numbers in exactly one way (ignoring order). 12 = 2² × 3 — there is no other way.

If n = p₁^a₁ × p₂^a₂ × ..., the number of divisors is (a₁+1)(a₂+1)... Each divisor is formed by choosing any exponent from 0 to aᵢ for each prime.

No. 1 is neither prime nor composite. If 1 were prime, the Fundamental Theorem would fail because 12 could be written as 2²×3 or 1×2²×3, destroying uniqueness.

RSA encryption relies on multiplying two large primes being easy, but factorizing the product back being computationally very hard. Your secure bank connection uses keys based on primes with hundreds of digits.

Prime Factorization Calculator

How to Use

Prime Factorization Method

Worked Example

Frequently Asked Questions

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