360
- Input
- 360
- Expected output
- 2³ × 3² × 5
Highly composite number — many divisors.
prime factorization of integers
Prime Factorization — Decompose into Prime Factors
By the Fundamental Theorem of Arithmetic, every integer > 1 has a unique prime factorization. E.g. 360 = 2³ × 3² × 5.
Fundamental Theorem of Arithmetic
- Every integer greater than 1 can be written as a product of primes in a unique way (disregarding order). This uniqueness is the foundation of all number theory.
- Prime factorization is used in cryptography (RSA), fraction simplification (via GCD), and LCM computation.
Examples
Perfect square
- Input
- 1764
- Expected output
- 2² × 3² × 7²
All exponents are even → perfect square.
Full tool FAQ
A prime number is an integer greater than 1 that has no positive integer divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13…
Frequently asked questions
How to check if a number is a perfect square?
In the prime factorization, a number is a perfect square if all exponents are even. 36 = 2² × 3² ✓. 12 = 2² × 3 ✗.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.