Break a whole number into its prime factors, check whether it is prime, and count and add up all of its divisors.
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With whole number 360, the prime factorisation is 2³ × 3² × 5.
| Whole number | 360 |
|---|
| Prime factorisation | 2³ × 3² × 5 |
|---|---|
| Prime number? | No |
| Distinct prime factors | 3 |
| Prime factors counted with repeats | 6 |
| Number of divisors | 24 |
| Sum of all divisors | 1,170 |
Every whole number above 1 can be written as a product of prime numbers in exactly one way, apart from order. The calculator finds the primes by trial division up to the square root of the number, which is quick for any number up to one million million. From the exponents it works out how many divisors the number has and their total.
n = p₁^e₁ × p₂^e₂ × … Number of divisors = (e₁ + 1)(e₂ + 1)… Sum of divisors = Π (p^(e+1) − 1) ÷ (p − 1). Every whole number above 1 can be written as a product of prime numbers in exactly one way, apart from order. The calculator finds the primes by trial division up to the square root of the number, which is quick for any number up to one million million. From the exponents it works out how many divisors the number has and their total.
With whole number 360, the prime factorisation is 2³ × 3² × 5. Prime number?: No; Distinct prime factors: 3; Prime factors counted with repeats: 6; Number of divisors: 24; Sum of all divisors: 1,170.
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360 = 2³ × 3² × 5. It has (3 + 1)(2 + 1)(1 + 1) = 24 divisors, and they add up to 1,170.
No. A prime has exactly two divisors, 1 and itself, and 1 has only one. Excluding 1 keeps every number's prime factorisation unique.
Divide by 2 as many times as possible, then by 3, 5, 7 and so on. Stop when the divisor squared exceeds what remains; any remainder above 1 is itself prime.