About this calculator
Enter a whole number and this calculator writes it as a product of prime factors, tells you whether it is prime, and lists its divisors.
It works for any number up to 1,000,000,000,000 and shows the steps.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
360
- Prime factorisation
- 2³ × 3² × 5
- Is it prime?
- No
- Number of divisors
- 24
- Sum of divisors
- 1,170
- All the 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
360 = 2 × 2 × 2 × 3 × 3 × 5, which is 2³ × 3² × 5.
Show the working
- Divide by the smallest prime that goes in (2, 3, 5, 7, …) and repeat with the answer until you reach 1.
- The primes that divided it, multiplied together, are 2 × 2 × 2 × 3 × 3 × 5.
- Writing repeats as powers gives 2³ × 3² × 5.
- Divisors: add 1 to each power and multiply: 4 × 3 × 2 = 24.
97 (a prime)
- Prime factorisation
- 97 (it is prime)
- Is it prime?
- Yes
- Number of divisors
- 2
- Sum of divisors
- 98
- All the divisors
- 1, 97
97 is a prime number: its only divisors are 1 and itself.
Show the working
- Try dividing by each prime up to √97 (about 9). None divides it exactly, so it is prime.
1,000,000
- Prime factorisation
- 2⁶ × 5⁶
- Is it prime?
- No
- Number of divisors
- 49
- Sum of divisors
- 2,480,437
- All the divisors
- 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1,000, 1,250, 1,600, 2,000, 2,500, 3,125, 4,000, 5,000, 6,250, 8,000, 10,000, 12,500, 15,625, 20,000, 25,000, 31,250, 40,000, 50,000, 62,500, 100,000, 125,000, 200,000, 250,000, 500,000, 1,000,000
1,000,000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5 × 5, which is 2⁶ × 5⁶.
Show the working
- Divide by the smallest prime that goes in (2, 3, 5, 7, …) and repeat with the answer until you reach 1.
- The primes that divided it, multiplied together, are 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5 × 5.
- Writing repeats as powers gives 2⁶ × 5⁶.
- Divisors: add 1 to each power and multiply: 7 × 7 = 49.
What is a prime factor?
A prime number has exactly two divisors: 1 and itself (2, 3, 5, 7, 11…). Every whole number above 1 is either prime or can be written in exactly one way as a product of primes. That is the fundamental theorem of arithmetic. For example, 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
How to factorise by hand
Divide by the smallest prime that goes in exactly (try 2, then 3, 5, 7…), and repeat with the answer until you reach 1. You only need to try primes up to the square root of the number: if none divides it, the number is prime.
Counting and adding divisors
Once you have the factorisation, the number of divisors is the product of (each power + 1). For 360 = 2³ × 3² × 5¹ that is 4 × 3 × 2 = 24 divisors. The divisors add up to 1,170.
Frequently asked questions
What is the prime factorisation of 360?
2³ × 3² × 5.
Is 1 a prime number?
No. A prime has exactly two divisors, and 1 has only one.
Is 2 prime?
Yes, and it is the only even prime number.
How large a number can it handle?
Up to 1,000,000,000,000 (one trillion).
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.