What are the divisors of 743?

1, 743

There is a total of 2 positive divisors.
The sum of these divisors is 744.
The arithmetic mean is 372.

2 odd divisors

1, 743

How to compute the divisors of 743?

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 743 by each of the numbers from 1 to 743 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)

743 / 1 = 743 (the remainder is 0, so 1 is a divisor of 743)
743 / 2 = 371.5 (the remainder is 1, so 2 is not a divisor of 743)
743 / 3 = 247.66666666667 (the remainder is 2, so 3 is not a divisor of 743)
...
743 / 742 = 1.0013477088949 (the remainder is 1, so 742 is not a divisor of 743)
743 / 743 = 1 (the remainder is 0, so 743 is a divisor of 743)

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 743 (i.e. 27.258026340878). 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 $\frac{N}{d} = D$ )

743 / 1 = 743 (the remainder is 0, so 1 and 743 are divisors of 743)
743 / 2 = 371.5 (the remainder is 1, so 2 is not a divisor of 743)
743 / 3 = 247.66666666667 (the remainder is 2, so 3 is not a divisor of 743)
...
743 / 26 = 28.576923076923 (the remainder is 15, so 26 is not a divisor of 743)
743 / 27 = 27.518518518519 (the remainder is 14, so 27 is not a divisor of 743)