What are the divisors of 974?

1, 2, 487, 974

2 even divisors

2, 974

2 odd divisors

1, 487

How to compute the divisors of 974?

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 974 by each of the numbers from 1 to 974 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)

  • 974 / 1 = 974 (the remainder is 0, so 1 is a divisor of 974)
  • 974 / 2 = 487 (the remainder is 0, so 2 is a divisor of 974)
  • 974 / 3 = 324.66666666667 (the remainder is 2, so 3 is not a divisor of 974)
  • ...
  • 974 / 973 = 1.0010277492292 (the remainder is 1, so 973 is not a divisor of 974)
  • 974 / 974 = 1 (the remainder is 0, so 974 is a divisor of 974)

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 974 (i.e. 31.208973068654). 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 )

  • 974 / 1 = 974 (the remainder is 0, so 1 and 974 are divisors of 974)
  • 974 / 2 = 487 (the remainder is 0, so 2 and 487 are divisors of 974)
  • 974 / 3 = 324.66666666667 (the remainder is 2, so 3 is not a divisor of 974)
  • ...
  • 974 / 30 = 32.466666666667 (the remainder is 14, so 30 is not a divisor of 974)
  • 974 / 31 = 31.41935483871 (the remainder is 13, so 31 is not a divisor of 974)