What are the divisors of 3554?

1, 2, 1777, 3554

There is a total of 4 positive divisors.
The sum of these divisors is 5334.
The arithmetic mean is 1333.5.

2 even divisors

2, 3554

2 odd divisors

1, 1777

How to compute the divisors of 3554?

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 3554 by each of the numbers from 1 to 3554 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)

3554 / 1 = 3554 (the remainder is 0, so 1 is a divisor of 3554)
3554 / 2 = 1777 (the remainder is 0, so 2 is a divisor of 3554)
3554 / 3 = 1184.6666666667 (the remainder is 2, so 3 is not a divisor of 3554)
...
3554 / 3553 = 1.0002814522938 (the remainder is 1, so 3553 is not a divisor of 3554)
3554 / 3554 = 1 (the remainder is 0, so 3554 is a divisor of 3554)

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 3554 (i.e. 59.615434243156). 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 $\frac{N}{d} = D$ )

3554 / 1 = 3554 (the remainder is 0, so 1 and 3554 are divisors of 3554)
3554 / 2 = 1777 (the remainder is 0, so 2 and 1777 are divisors of 3554)
3554 / 3 = 1184.6666666667 (the remainder is 2, so 3 is not a divisor of 3554)
...
3554 / 58 = 61.275862068966 (the remainder is 16, so 58 is not a divisor of 3554)
3554 / 59 = 60.237288135593 (the remainder is 14, so 59 is not a divisor of 3554)