What are the divisors of 5351?

1, 5351

2 odd divisors

1, 5351

How to compute the divisors of 5351?

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 5351 by each of the numbers from 1 to 5351 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)

  • 5351 / 1 = 5351 (the remainder is 0, so 1 is a divisor of 5351)
  • 5351 / 2 = 2675.5 (the remainder is 1, so 2 is not a divisor of 5351)
  • 5351 / 3 = 1783.6666666667 (the remainder is 2, so 3 is not a divisor of 5351)
  • ...
  • 5351 / 5350 = 1.0001869158879 (the remainder is 1, so 5350 is not a divisor of 5351)
  • 5351 / 5351 = 1 (the remainder is 0, so 5351 is a divisor of 5351)

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 5351 (i.e. 73.150529731506). 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 )

  • 5351 / 1 = 5351 (the remainder is 0, so 1 and 5351 are divisors of 5351)
  • 5351 / 2 = 2675.5 (the remainder is 1, so 2 is not a divisor of 5351)
  • 5351 / 3 = 1783.6666666667 (the remainder is 2, so 3 is not a divisor of 5351)
  • ...
  • 5351 / 72 = 74.319444444444 (the remainder is 23, so 72 is not a divisor of 5351)
  • 5351 / 73 = 73.301369863014 (the remainder is 22, so 73 is not a divisor of 5351)