What are the divisors of 2741?

1, 2741

2 odd divisors

1, 2741

How to compute the divisors of 2741?

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 2741 by each of the numbers from 1 to 2741 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)

  • 2741 / 1 = 2741 (the remainder is 0, so 1 is a divisor of 2741)
  • 2741 / 2 = 1370.5 (the remainder is 1, so 2 is not a divisor of 2741)
  • 2741 / 3 = 913.66666666667 (the remainder is 2, so 3 is not a divisor of 2741)
  • ...
  • 2741 / 2740 = 1.0003649635036 (the remainder is 1, so 2740 is not a divisor of 2741)
  • 2741 / 2741 = 1 (the remainder is 0, so 2741 is a divisor of 2741)

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 2741 (i.e. 52.354560450834). 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 )

  • 2741 / 1 = 2741 (the remainder is 0, so 1 and 2741 are divisors of 2741)
  • 2741 / 2 = 1370.5 (the remainder is 1, so 2 is not a divisor of 2741)
  • 2741 / 3 = 913.66666666667 (the remainder is 2, so 3 is not a divisor of 2741)
  • ...
  • 2741 / 51 = 53.745098039216 (the remainder is 38, so 51 is not a divisor of 2741)
  • 2741 / 52 = 52.711538461538 (the remainder is 37, so 52 is not a divisor of 2741)