What are the divisors of 554?

1, 2, 277, 554

There is a total of 4 positive divisors.
The sum of these divisors is 834.
The arithmetic mean is 208.5.

2 even divisors

2, 554

2 odd divisors

1, 277

How to compute the divisors of 554?

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 554 by each of the numbers from 1 to 554 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

554 / 1 = 554 (the remainder is 0, so 1 is a divisor of 554)
554 / 2 = 277 (the remainder is 0, so 2 is a divisor of 554)
554 / 3 = 184.66666666667 (the remainder is 2, so 3 is not a divisor of 554)
...
554 / 553 = 1.001808318264 (the remainder is 1, so 553 is not a divisor of 554)
554 / 554 = 1 (the remainder is 0, so 554 is a divisor of 554)

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 554 (i.e. 23.53720459188). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

554 / 1 = 554 (the remainder is 0, so 1 and 554 are divisors of 554)
554 / 2 = 277 (the remainder is 0, so 2 and 277 are divisors of 554)
554 / 3 = 184.66666666667 (the remainder is 2, so 3 is not a divisor of 554)
...
554 / 22 = 25.181818181818 (the remainder is 4, so 22 is not a divisor of 554)
554 / 23 = 24.086956521739 (the remainder is 2, so 23 is not a divisor of 554)