Prime Factorization Calculator
Enter a whole number to write it as a product of primes. You get the repeated division steps, the exponent form and the count of prime factors. It also tells you if the number is prime.
Last updated November 4, 2026
A whole number from 1 to 1,000,000,000,000.
Result
360 = 2³ × 3² × 5
| Measure | Value |
|---|---|
| Prime factors | 2 × 2 × 2 × 3 × 3 × 5 |
| Exponent form | 2³ × 3² × 5 |
| Total prime factors | 6 |
| Distinct primes | 3 |
| Prime or composite | 360 is composite |
Factors are found by trial division, from the smallest prime up. Total prime factors counts repeats; distinct primes does not.
Show the work
Formula: Divide by the smallest prime that fits, repeat with the quotient until you reach 1.
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
- Primes used: 2 × 2 × 2 × 3 × 3 × 5. Multiplying them gives 360.
Result: 360 = 2³ × 3² × 5
How prime factorization works
n = p₁ × p₂ × … × pₖ, each p a prime
e.g. 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Divide the number by the smallest prime that goes into it evenly, then repeat with the quotient until you reach 1. The primes you divided by are the prime factors. Every whole number above 1 has exactly one such list, apart from order.
Exponent form groups repeats: three 2s become 2³. The total count includes repeats (360 has 6), while distinct primes counts each prime once (360 has 3).
To list every factor or factor pair instead, use the Factor Calculator. This page focuses on the prime breakdown.
See how we calculate for the formulas, sources and review schedule behind every calculator.
How to use the Prime Factorization Calculator
- Enter a whole number from 1 to 1,000,000,000,000.
- Read the prime factors, exponent form and counts.
- Open Show the work to follow each division down to 1.
- Use Copy or Share to keep the result.
Worked example
360 divides by 2 three times (180, 90, 45), by 3 twice (15, 5), then by 5 to reach 1, so 360 = 2³ × 3² × 5.
| Number | Exponent form | Total prime factors | Distinct primes |
|---|---|---|---|
| 60 | 2² × 3 × 5 | 4 | 3 |
| 84 | 2² × 3 × 7 | 4 | 3 |
| 360 | 2³ × 3² × 5 | 6 | 3 |
| 1001 | 7 × 11 × 13 | 3 | 3 |
| 1024 | 2¹⁰ | 10 | 1 |
| 97 | 97 (prime) | 1 | 1 |
Frequently asked questions
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself. The number 1 has only one, so it is neither prime nor composite, and it has no prime factors.
How do I know if a number is prime?
If its factorization is just the number itself, it is prime. This calculator shows that case as "is prime".
What is the difference between a factor tree and repeated division?
Both reach the same primes. A tree splits a number into any two factors, while repeated division always uses the smallest prime first.
How large a number can I enter?
Up to 1,000,000,000,000. Larger numbers could take too long to factor by trial division, so they are not accepted.