What are the divisors of 5407?

1, 5407

2 odd divisors

1, 5407

How to compute the divisors of 5407?

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 5407 by each of the numbers from 1 to 5407 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)

  • 5407 / 1 = 5407 (the remainder is 0, so 1 is a divisor of 5407)
  • 5407 / 2 = 2703.5 (the remainder is 1, so 2 is not a divisor of 5407)
  • 5407 / 3 = 1802.3333333333 (the remainder is 1, so 3 is not a divisor of 5407)
  • ...
  • 5407 / 5406 = 1.0001849796522 (the remainder is 1, so 5406 is not a divisor of 5407)
  • 5407 / 5407 = 1 (the remainder is 0, so 5407 is a divisor of 5407)

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 5407 (i.e. 73.532305825399). 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 )

  • 5407 / 1 = 5407 (the remainder is 0, so 1 and 5407 are divisors of 5407)
  • 5407 / 2 = 2703.5 (the remainder is 1, so 2 is not a divisor of 5407)
  • 5407 / 3 = 1802.3333333333 (the remainder is 1, so 3 is not a divisor of 5407)
  • ...
  • 5407 / 72 = 75.097222222222 (the remainder is 7, so 72 is not a divisor of 5407)
  • 5407 / 73 = 74.068493150685 (the remainder is 5, so 73 is not a divisor of 5407)