What are the divisors of 740?

1, 2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740

There is a total of 12 positive divisors.
The sum of these divisors is 1596.
The arithmetic mean is 133.

8 even divisors

2, 4, 10, 20, 74, 148, 370, 740

4 odd divisors

1, 5, 37, 185

How to compute the divisors of 740?

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 740 by each of the numbers from 1 to 740 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)

740 / 1 = 740 (the remainder is 0, so 1 is a divisor of 740)
740 / 2 = 370 (the remainder is 0, so 2 is a divisor of 740)
740 / 3 = 246.66666666667 (the remainder is 2, so 3 is not a divisor of 740)
...
740 / 739 = 1.0013531799729 (the remainder is 1, so 739 is not a divisor of 740)
740 / 740 = 1 (the remainder is 0, so 740 is a divisor of 740)

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 740 (i.e. 27.202941017471). 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 $\frac{N}{d} = D$ )

740 / 1 = 740 (the remainder is 0, so 1 and 740 are divisors of 740)
740 / 2 = 370 (the remainder is 0, so 2 and 370 are divisors of 740)
740 / 3 = 246.66666666667 (the remainder is 2, so 3 is not a divisor of 740)
...
740 / 26 = 28.461538461538 (the remainder is 12, so 26 is not a divisor of 740)
740 / 27 = 27.407407407407 (the remainder is 11, so 27 is not a divisor of 740)