What are the divisors of 2963?

1, 2963

2 odd divisors

1, 2963

How to compute the divisors of 2963?

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 2963 by each of the numbers from 1 to 2963 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)

  • 2963 / 1 = 2963 (the remainder is 0, so 1 is a divisor of 2963)
  • 2963 / 2 = 1481.5 (the remainder is 1, so 2 is not a divisor of 2963)
  • 2963 / 3 = 987.66666666667 (the remainder is 2, so 3 is not a divisor of 2963)
  • ...
  • 2963 / 2962 = 1.0003376097232 (the remainder is 1, so 2962 is not a divisor of 2963)
  • 2963 / 2963 = 1 (the remainder is 0, so 2963 is a divisor of 2963)

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 2963 (i.e. 54.433445601027). 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 )

  • 2963 / 1 = 2963 (the remainder is 0, so 1 and 2963 are divisors of 2963)
  • 2963 / 2 = 1481.5 (the remainder is 1, so 2 is not a divisor of 2963)
  • 2963 / 3 = 987.66666666667 (the remainder is 2, so 3 is not a divisor of 2963)
  • ...
  • 2963 / 53 = 55.905660377358 (the remainder is 48, so 53 is not a divisor of 2963)
  • 2963 / 54 = 54.87037037037 (the remainder is 47, so 54 is not a divisor of 2963)