What are the divisors of 477?

1, 3, 9, 53, 159, 477

6 odd divisors

1, 3, 9, 53, 159, 477

How to compute the divisors of 477?

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 477 by each of the numbers from 1 to 477 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)

  • 477 / 1 = 477 (the remainder is 0, so 1 is a divisor of 477)
  • 477 / 2 = 238.5 (the remainder is 1, so 2 is not a divisor of 477)
  • 477 / 3 = 159 (the remainder is 0, so 3 is a divisor of 477)
  • ...
  • 477 / 476 = 1.0021008403361 (the remainder is 1, so 476 is not a divisor of 477)
  • 477 / 477 = 1 (the remainder is 0, so 477 is a divisor of 477)

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 477 (i.e. 21.840329667842). 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 )

  • 477 / 1 = 477 (the remainder is 0, so 1 and 477 are divisors of 477)
  • 477 / 2 = 238.5 (the remainder is 1, so 2 is not a divisor of 477)
  • 477 / 3 = 159 (the remainder is 0, so 3 and 159 are divisors of 477)
  • ...
  • 477 / 20 = 23.85 (the remainder is 17, so 20 is not a divisor of 477)
  • 477 / 21 = 22.714285714286 (the remainder is 15, so 21 is not a divisor of 477)