What are the divisors of 4526?

1, 2, 31, 62, 73, 146, 2263, 4526

4 even divisors

2, 62, 146, 4526

4 odd divisors

1, 31, 73, 2263

How to compute the divisors of 4526?

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 4526 by each of the numbers from 1 to 4526 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)

  • 4526 / 1 = 4526 (the remainder is 0, so 1 is a divisor of 4526)
  • 4526 / 2 = 2263 (the remainder is 0, so 2 is a divisor of 4526)
  • 4526 / 3 = 1508.6666666667 (the remainder is 2, so 3 is not a divisor of 4526)
  • ...
  • 4526 / 4525 = 1.0002209944751 (the remainder is 1, so 4525 is not a divisor of 4526)
  • 4526 / 4526 = 1 (the remainder is 0, so 4526 is a divisor of 4526)

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 4526 (i.e. 67.275552766217). 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 )

  • 4526 / 1 = 4526 (the remainder is 0, so 1 and 4526 are divisors of 4526)
  • 4526 / 2 = 2263 (the remainder is 0, so 2 and 2263 are divisors of 4526)
  • 4526 / 3 = 1508.6666666667 (the remainder is 2, so 3 is not a divisor of 4526)
  • ...
  • 4526 / 66 = 68.575757575758 (the remainder is 38, so 66 is not a divisor of 4526)
  • 4526 / 67 = 67.55223880597 (the remainder is 37, so 67 is not a divisor of 4526)