Prime Factorisation Calculator
Easily find the prime factors of any number with our free online tool. Get instant results in standard list and exponential form, perfect for maths homework and problem-solving.
Find Your Prime Factors
Enter any whole number greater than 1 below to instantly see its prime factorisation, exponential notation, and whether the number itself is prime.
Factorisation Results
Based on your entered number
How to Find Prime Factors
Learning the manual method of prime factorisation helps build a strong foundation in arithmetic and number theory.
Start with the Smallest Prime
Begin by dividing your number by the smallest prime number, which is 2. If the number is even, it will divide evenly.
Repeat the Division
Take the quotient (the result of the division) and divide it by 2 again. Keep doing this until the number is no longer divisible by 2.
Move to the Next Prime
Once the number is odd, move to the next prime number (3, then 5, 7, 11, etc.) and repeat the division process until the final quotient is 1.
Write in Exponential Form
Group the identical prime factors together and write them with exponents. For example, 2 × 2 × 2 becomes 2³.
Essential Divisibility Rules
Use these quick rules to determine if a number can be divided by small primes without using a calculator.
| Prime Number | Divisibility Rule | Example |
|---|---|---|
| 2 | The last digit is even (0, 2, 4, 6, or 8). | 346 is divisible by 2 (ends in 6). |
| 3 | The sum of all digits is divisible by 3. | 123 is divisible by 3 (1+2+3 = 6). |
| 5 | The last digit is 0 or 5. | 895 is divisible by 5 (ends in 5). |
| 7 | Double the last digit, subtract it from the rest of the number. If the result is divisible by 7, so is the original. | 203: (20 – (3×2)) = 14. Divisible by 7. |
| 11 | The alternating sum of the digits is divisible by 11. | 913: (9 – 1 + 3) = 11. Divisible by 11. |
Prime Factorisation FAQ
Answers to the most frequently asked questions about prime numbers, factors, and mathematical decomposition.
Prime factorisation is the process of breaking down a composite number into a multiplication of its prime factors. A prime factor is a prime number that divides the original number exactly, without leaving a remainder.
Start by dividing the number by the smallest prime number (2). If it divides evenly, write down 2 and divide the result by 2 again. If not, move to the next prime number (3, 5, 7, etc.) and repeat the process until the final quotient is 1.
The number 1 is neither prime nor composite. By definition, it has no prime factors, as prime numbers must be strictly greater than 1 and have exactly two distinct positive divisors.
Prime factorisation is fundamental in mathematics. It is used to find the Greatest Common Divisor (GCD) and Least Common Multiple (LCM), simplify fractions, and forms the basis of modern cryptographic security systems like RSA encryption.