Supports integers from -1,000,000,000,000 to 1,000,000,000,000.
What is factorisation?
Factorisation is the process of breaking a number into smaller numbers that multiply together to produce the original value. For example, 12 can be written as 3 × 4, 2 × 6, or as prime factors 2 × 2 × 3. A factorise calculator helps you do this instantly and accurately.
Prime factors vs. factor pairs
- Prime factors are factors that are prime numbers (only divisible by 1 and themselves).
- Factor pairs are two integers whose product equals the original number, like (3, 4) for 12.
- Prime factorisation is unique for each positive integer greater than 1.
How to use this factorise calculator
- Type a whole number in the input box.
- Click Factorise.
- Read the output for prime factorisation, expanded factors, divisor count, full divisor list, and factor pairs.
The calculator also handles negative integers. For negative numbers, it includes -1 in the prime factorisation.
Worked examples
Example 1: 360
360 factorises to 23 × 32 × 5. Expanded form: 2 × 2 × 2 × 3 × 3 × 5.
Example 2: 997
997 is a prime number, so its prime factorisation is simply 997. Its only positive factors are 1 and 997.
Example 3: -84
-84 factorises as -1 × 22 × 3 × 7. The positive factor pairs come from 84, and one value in each pair can be negative to make the product -84.
Why factorisation matters
- Simplifying fractions: cancel common factors quickly.
- Number theory: understand divisibility, primes, and modular arithmetic.
- Algebra foundations: number factor skills transfer to polynomial factorisation.
- Cryptography basics: prime factors are central to many security systems.
Common mistakes to avoid
- Forgetting that 1 is not a prime number.
- Mixing up factor pairs and prime factors.
- Ignoring sign when factorising negative numbers.
- Stopping too early before fully breaking numbers into primes.
FAQ
Can I factorise zero?
Zero does not have a finite prime factorisation, because every non-zero integer divides 0.
Does every number have a unique prime factorisation?
Every integer greater than 1 has one unique prime factorisation (up to order). This is the Fundamental Theorem of Arithmetic.
Can this be used for polynomial factorisation?
This specific tool is for integer factorisation. Polynomial factorisation follows similar ideas but requires different algebraic methods.