What are the divisors of 583?

1, 11, 53, 583

4 odd divisors

1, 11, 53, 583

How to compute the divisors of 583?

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 583 by each of the numbers from 1 to 583 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)

  • 583 / 1 = 583 (the remainder is 0, so 1 is a divisor of 583)
  • 583 / 2 = 291.5 (the remainder is 1, so 2 is not a divisor of 583)
  • 583 / 3 = 194.33333333333 (the remainder is 1, so 3 is not a divisor of 583)
  • ...
  • 583 / 582 = 1.0017182130584 (the remainder is 1, so 582 is not a divisor of 583)
  • 583 / 583 = 1 (the remainder is 0, so 583 is a divisor of 583)

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 583 (i.e. 24.145392935299). 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 )

  • 583 / 1 = 583 (the remainder is 0, so 1 and 583 are divisors of 583)
  • 583 / 2 = 291.5 (the remainder is 1, so 2 is not a divisor of 583)
  • 583 / 3 = 194.33333333333 (the remainder is 1, so 3 is not a divisor of 583)
  • ...
  • 583 / 23 = 25.347826086957 (the remainder is 8, so 23 is not a divisor of 583)
  • 583 / 24 = 24.291666666667 (the remainder is 7, so 24 is not a divisor of 583)