What are the divisors of 746?

1, 2, 373, 746

There is a total of 4 positive divisors.
The sum of these divisors is 1122.
The arithmetic mean is 280.5.

2 even divisors

2, 746

2 odd divisors

1, 373

How to compute the divisors of 746?

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 746 by each of the numbers from 1 to 746 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)

746 / 1 = 746 (the remainder is 0, so 1 is a divisor of 746)
746 / 2 = 373 (the remainder is 0, so 2 is a divisor of 746)
746 / 3 = 248.66666666667 (the remainder is 2, so 3 is not a divisor of 746)
...
746 / 745 = 1.0013422818792 (the remainder is 1, so 745 is not a divisor of 746)
746 / 746 = 1 (the remainder is 0, so 746 is a divisor of 746)

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 746 (i.e. 27.313000567495). 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 $\frac{N}{d} = D$ )

746 / 1 = 746 (the remainder is 0, so 1 and 746 are divisors of 746)
746 / 2 = 373 (the remainder is 0, so 2 and 373 are divisors of 746)
746 / 3 = 248.66666666667 (the remainder is 2, so 3 is not a divisor of 746)
...
746 / 26 = 28.692307692308 (the remainder is 18, so 26 is not a divisor of 746)
746 / 27 = 27.62962962963 (the remainder is 17, so 27 is not a divisor of 746)