What are the divisors of 4899?

1, 3, 23, 69, 71, 213, 1633, 4899

8 odd divisors

1, 3, 23, 69, 71, 213, 1633, 4899

How to compute the divisors of 4899?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

N mod M = 0

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4899 by each of the numbers from 1 to 4899 to determine which ones have a remainder equal to 0.

Remainder = N ( M × N M )

(where N M is the integer part of the quotient)

  • 4899 / 1 = 4899 (the remainder is 0, so 1 is a divisor of 4899)
  • 4899 / 2 = 2449.5 (the remainder is 1, so 2 is not a divisor of 4899)
  • 4899 / 3 = 1633 (the remainder is 0, so 3 is a divisor of 4899)
  • ...
  • 4899 / 4898 = 1.0002041649653 (the remainder is 1, so 4898 is not a divisor of 4899)
  • 4899 / 4899 = 1 (the remainder is 0, so 4899 is a divisor of 4899)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4899 (i.e. 69.992856778388). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

D × d = N

(thus, if N D = d , then N d = D )

  • 4899 / 1 = 4899 (the remainder is 0, so 1 and 4899 are divisors of 4899)
  • 4899 / 2 = 2449.5 (the remainder is 1, so 2 is not a divisor of 4899)
  • 4899 / 3 = 1633 (the remainder is 0, so 3 and 1633 are divisors of 4899)
  • ...
  • 4899 / 68 = 72.044117647059 (the remainder is 3, so 68 is not a divisor of 4899)
  • 4899 / 69 = 71 (the remainder is 0, so 69 and 71 are divisors of 4899)