What are the divisors of 4670?

1, 2, 5, 10, 467, 934, 2335, 4670

4 even divisors

2, 10, 934, 4670

4 odd divisors

1, 5, 467, 2335

How to compute the divisors of 4670?

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 4670 by each of the numbers from 1 to 4670 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)

  • 4670 / 1 = 4670 (the remainder is 0, so 1 is a divisor of 4670)
  • 4670 / 2 = 2335 (the remainder is 0, so 2 is a divisor of 4670)
  • 4670 / 3 = 1556.6666666667 (the remainder is 2, so 3 is not a divisor of 4670)
  • ...
  • 4670 / 4669 = 1.000214178625 (the remainder is 1, so 4669 is not a divisor of 4670)
  • 4670 / 4670 = 1 (the remainder is 0, so 4670 is a divisor of 4670)

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 4670 (i.e. 68.33739825308). 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 )

  • 4670 / 1 = 4670 (the remainder is 0, so 1 and 4670 are divisors of 4670)
  • 4670 / 2 = 2335 (the remainder is 0, so 2 and 2335 are divisors of 4670)
  • 4670 / 3 = 1556.6666666667 (the remainder is 2, so 3 is not a divisor of 4670)
  • ...
  • 4670 / 67 = 69.701492537313 (the remainder is 47, so 67 is not a divisor of 4670)
  • 4670 / 68 = 68.676470588235 (the remainder is 46, so 68 is not a divisor of 4670)