[Golang] Calculate Number of Divisors


Assume n is a natural number, calculate the number of divisors of n.

Let the prime factorization of n be:

n = p1a1 × p2a2 × ... × pkak

number of divisors of n is:

(a1 + 1)(a2 + 1)...(ak + 1)

Prime Factorization

The following code will return prime factorization of a given number n:

// Prime factorization of a given number
//
// A map is returned.
//
//   key of map: prime
//   value of map: prime exponents
//
func PrimeFactorization(n int) (pfs map[int]int) {
      pfs = make(map[int]int)

      // Get the number of 2s that divide n
      for n%2 == 0 {
              if _, ok := pfs[2]; ok {
                      pfs[2] += 1
              } else {
                      pfs[2] = 1
              }
              n = n / 2
      }

      // n must be odd at this point. so we can skip one element
      // (note i = i + 2)
      for i := 3; i*i <= n; i = i + 2 {
              // while i divides n, append i and divide n
              for n%i == 0 {
                      if _, ok := pfs[i]; ok {
                              pfs[i] += 1
                      } else {
                              pfs[i] = 1
                      }
                      n = n / i
              }
      }

      // This condition is to handle the case when n is a prime number
      // greater than 2
      if n > 2 {
              pfs[n] = 1
      }

      return
}

See [2] [3] for more details.

Number of Divisors

Based on the result of prime factorization of previous section, we can calculate number of divisors of a given number n as follows:

// Calculate number of divisors of a given number
func NumberOfDivisors(n int) int {
      pfs := PrimeFactorization(n)

      num := 1
      for _, exponents := range pfs {
              num *= (exponents + 1)
      }

      return num
}

See [1] for more details.