Everything is worked out in your browser and saved on this device for next time.
About the prime factorization calculator
A prime number can only be divided by 1 and itself: 2, 3, 5, 7, 11, 13 and so on. Every whole number bigger than 1 can be written as prime numbers multiplied together. This is its prime factorization, and there is only one way to do it.
For a number you type, this calculator shows:
- The prime factorization in short form, like 2³ × 3² × 5
- is it a prime number? — yes or no
- The factorization written out, like 2 × 2 × 2 × 3 × 3 × 5
- The number of divisors
- The next prime number
- The list of all divisors (when there are 120 or fewer)
It works for whole numbers from 2 up to 1,000,000,000,000 (one trillion).
Features
- Big numbers — any whole number from 2 up to one trillion
- Two forms — short form with powers, like 2³ × 3² × 5, and written out
- Prime check — is it a prime number? yes or no
- Divisors — the number of divisors, and the full list when there are 120 or fewer
- Next prime number — the first prime after your number
- Quick numbers — tap 60, 84, 100, 360, 1001, 65536 or 97
- Copy — copy the result with one click
- Private — it works in your browser, nothing is uploaded, and your number is saved on this device
How to use it
- Type your number in Whole number (up to 1,000,000,000,000)
- Or tap one of the quick numbers: 60, 84, 100, 360, 1001, 65536, 97
- The result updates while you type
- Press Copy to copy the result, or Start again to go back to 360
Example: 360
The tool opens with 360.
- Prime factorization: 2³ × 3² × 5
- Written out: 2 × 2 × 2 × 3 × 3 × 5
- Is it prime? No
- Number of divisors: 24
- Next prime number: 367
- Divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
More numbers
| Number | Prime factorization | Divisors | Next prime |
|---|---|---|---|
| 60 | 2² × 3 × 5 | 12 | 61 |
| 84 | 2² × 3 × 7 | 12 | 89 |
| 100 | 2² × 5² | 9 | 101 |
| 97 | 97 (prime) | 2 | 101 |
| 1001 | 7 × 11 × 13 | 8 | 1009 |
| 2026 | 2 × 1013 | 4 | 2027 |
| 65536 | 2¹⁶ | 17 | 65537 |
| 1000000 | 2⁶ × 5⁶ | 49 | 1000003 |
How to count the divisors
Take the powers in the prime factorization, add 1 to each, and multiply. For 360 = 2³ × 3² × 5¹ that is (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24 divisors.
Frequently asked questions
How do I find the prime factorization by hand?
Divide by the smallest prime that fits (2, then 3, then 5 …) and keep going with the answer. For 360: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5. So 360 = 2³ × 3² × 5.
Is 1 a prime number?
No. A prime needs exactly two different divisors, and 1 has only one. That is why the tool starts at 2.
Is 2 the only even prime?
Yes. Every other even number can be divided by 2, so it is not prime.
What is a factor tree?
It is a drawing of the same steps: split the number into two factors, then split each one again until only primes are left. The result is the same as this tool shows.
How is this used in school maths?
Prime factors help you find the greatest common factor and the least common multiple, and simplify fractions. For two or more numbers, use the GCF and LCM calculator.
Why is no divisor list shown for some numbers?
When a number has more than 120 divisors, the list would be too long, so only the count is shown.
Good to know
- Everything is worked out in your browser — nothing is sent anywhere
- Your last number is saved on this device
- Spaces and commas in the number are ignored, so 1,000,000 works
Related tools
- GCF and LCM Calculator — greatest common factor and least common multiple
- Fraction Calculator — simplify and add fractions
- Ratio Calculator — simplify a ratio
- Math Worksheet Generator — print practice sheets
- Number Base Converter — see the number in binary or hex
