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Prime Factorisation Calculator
Sign up to favourite this calculatorEnter a whole number greater than 1 to break it into its prime factors. The calculator shows the expanded factorisation, index form, factorisation steps and number of positive factors.
Enter a whole number
Prime factorisation
360 is a prime number — its only factors are 1 and itself.
Expanded form: 2 × 2 × 2 × 3 × 3 × 5
Number type
Composite numberDistinct prime factors
2, 3, 5Total prime factors
6Number of positive factors
24| Step | Value |
|---|---|
| Start with | 360 |
| Divide by 2 | 360 ÷ 2 = 180 |
| Divide by 2 | 180 ÷ 2 = 90 |
| Divide by 2 | 90 ÷ 2 = 45 |
| Divide by 3 | 45 ÷ 3 = 15 |
| Divide by 3 | 15 ÷ 3 = 5 |
| Remaining number | 5 is prime |
| Prime factors | 2 × 2 × 2 × 3 × 3 × 5 |
| Index form | 2³ × 3² × 5 |
| Step | Value |
|---|---|
| Prime factorisation | 2³ × 3² × 5¹ |
| Add 1 to each exponent | (3 + 1) × (2 + 1) × (1 + 1) |
| Multiply | 4 × 3 × 2 |
| Positive factors | 24 |
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Enter a whole number greater than 1. Grouping commas such as
1,000,000are fine. - Read the result: the prime factorisation in index form is the large figure, with the expanded form, whether the number is prime or composite, its distinct prime factors and its number of positive factors beside it.
- The first table shows every division used to factorise the number; the second shows how the number of positive factors is worked out.
- Use Reset to return to the starting number.
The calculation runs in the page as you type — nothing is sent to a server.
What do I need to enter?
- Number to factorise — a whole number from 2 up to 1,000,000,000. Grouping commas are ignored; decimals, negatives, 0 and 1 are rejected.
What do the results show?
- Prime factorisation — the main figure: your number as a product of primes, in index form such as 2³ × 3² × 5.
- Expanded form — the same product with every factor written out.
- Number type — whether the number is prime or composite.
- Distinct prime factors and total prime factors — the different primes used, and how many primes multiply together counting repeats.
- Number of positive factors — how many whole numbers divide it exactly, including 1 and itself.
- Working tables — each division used, and how the factor count is built from the exponents.
What is prime factorisation?
Prime factorisation writes a whole number as a multiplication of prime numbers. Repeated factors are usually collected into index form using powers.
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
- 2, 3 and 5 are the prime factors of 60.
- 2 appears twice, so it is written as 2².
- Every whole number greater than 1 has one unique prime factorisation, apart from the order of its factors.
What is a prime number?
A prime number has exactly two positive factors: 1 and itself. The first primes are 2, 3, 5, 7, 11, 13 and 17. If the number you enter is prime, its prime factorisation is the number itself — for example 97 = 97. A prime is not a number that "cannot be factorised"; its factorisation is simply a single prime.
How is the number of positive factors worked out?
Once a number is in index form, add 1 to each exponent and multiply the results. Every divisor of the number is made by choosing how many of each prime to include, from none up to its exponent.
factors of p₁ᵉ¹ × p₂ᵉ² × … = (e₁ + 1) × (e₂ + 1) × …
- Each exponent e is how many times that prime appears.
- The count includes 1 and the number itself.
Worked example: 360
360 is even, so divide by 2 repeatedly, then move to the next prime. The number left at the end, 5, is prime.
| Step | Value |
|---|---|
| Start with | 360 |
| Divide by 2 | 360 ÷ 2 = 180 |
| Divide by 2 | 180 ÷ 2 = 90 |
| Divide by 2 | 90 ÷ 2 = 45 |
| Divide by 3 | 45 ÷ 3 = 15 |
| Divide by 3 | 15 ÷ 3 = 5 |
| Remaining number | 5 is prime |
| Prime factors | 2 × 2 × 2 × 3 × 3 × 5 |
| Index form | 2³ × 3² × 5 |
So 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. The number of positive factors is:
| Step | Value |
|---|---|
| Prime factorisation | 2³ × 3² × 5¹ |
| Add 1 to each exponent | (3 + 1) × (2 + 1) × (1 + 1) |
| Multiply | 4 × 3 × 2 |
| Positive factors | 24 |
360 has three distinct prime factors (2, 3 and 5), six prime factors counting repeats, and 24 positive factors in total.
What this calculator covers
It factorises one positive whole number from 2 up to 1,000,000,000 using trial division, and shows the working. It does not draw a factor tree, take decimals or negative numbers, or list every divisor — only the count of them. Decimals are rejected rather than rounded, so12.9 is not treated as 13.
Frequently asked questions
How do you find the prime factorisation of a number?
Divide the number by the smallest prime that goes into it exactly, then keep dividing the result the same way until you are left with 1. The list of divisors you used is the prime factorisation. For 360: divide by 2 three times to reach 45, then by 3 twice to reach 5, which is prime — so 360 = 2 × 2 × 2 × 3 × 3 × 5.
What is prime factorisation in index form?
Index form (also called exponent form) groups repeated prime factors using powers. Instead of writing 2 × 2 × 2 × 3 × 3 × 5, you write 2³ × 3² × 5. The small raised number is how many times that prime appears. A prime that appears once is written without an exponent.
Is 1 a prime number?
No. A prime number has exactly two different positive factors: 1 and itself. The number 1 has only one factor, so it is neither prime nor composite and has no prime factorisation. This calculator asks for a whole number greater than 1.
What is the difference between a prime and a composite number?
A prime number greater than 1 has no divisors except 1 and itself — 2, 3, 5, 7, 11 and so on. A composite number has at least one other divisor, so it can be broken into a product of smaller primes. Every whole number greater than 1 is exactly one of the two.
How do you work out how many factors a number has?
Write the number in index form, add 1 to each exponent, and multiply the results. For 360 = 2³ × 3² × 5¹ that is (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24, so 360 has 24 positive factors. This counts every divisor, not just the prime ones.
What is the prime factorisation of 360?
360 = 2 × 2 × 2 × 3 × 3 × 5, which is 2³ × 3² × 5 in index form. It is a composite number with three distinct prime factors (2, 3 and 5), six prime factors counting repeats, and 24 positive factors in total.
What is the largest number this calculator can factorise?
One billion (1,000,000,000). The calculator uses trial division, which only tests divisors up to the square root of the number, so results stay instant across that whole range. Numbers above the limit are not accepted.
Last updated 25 October 2026.