What are the divisors of 4152?

1, 2, 3, 4, 6, 8, 12, 24, 173, 346, 519, 692, 1038, 1384, 2076, 4152

12 even divisors

2, 4, 6, 8, 12, 24, 346, 692, 1038, 1384, 2076, 4152

4 odd divisors

1, 3, 173, 519

How to compute the divisors of 4152?

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 4152 by each of the numbers from 1 to 4152 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)

  • 4152 / 1 = 4152 (the remainder is 0, so 1 is a divisor of 4152)
  • 4152 / 2 = 2076 (the remainder is 0, so 2 is a divisor of 4152)
  • 4152 / 3 = 1384 (the remainder is 0, so 3 is a divisor of 4152)
  • ...
  • 4152 / 4151 = 1.0002409058058 (the remainder is 1, so 4151 is not a divisor of 4152)
  • 4152 / 4152 = 1 (the remainder is 0, so 4152 is a divisor of 4152)

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 4152 (i.e. 64.436014774348). 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 )

  • 4152 / 1 = 4152 (the remainder is 0, so 1 and 4152 are divisors of 4152)
  • 4152 / 2 = 2076 (the remainder is 0, so 2 and 2076 are divisors of 4152)
  • 4152 / 3 = 1384 (the remainder is 0, so 3 and 1384 are divisors of 4152)
  • ...
  • 4152 / 63 = 65.904761904762 (the remainder is 57, so 63 is not a divisor of 4152)
  • 4152 / 64 = 64.875 (the remainder is 56, so 64 is not a divisor of 4152)