What are the divisors of 2978?

1, 2, 1489, 2978

There is a total of 4 positive divisors.
The sum of these divisors is 4470.
The arithmetic mean is 1117.5.

2 even divisors

2, 2978

2 odd divisors

1, 1489

How to compute the divisors of 2978?

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 2978 by each of the numbers from 1 to 2978 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)

2978 / 1 = 2978 (the remainder is 0, so 1 is a divisor of 2978)
2978 / 2 = 1489 (the remainder is 0, so 2 is a divisor of 2978)
2978 / 3 = 992.66666666667 (the remainder is 2, so 3 is not a divisor of 2978)
...
2978 / 2977 = 1.0003359086329 (the remainder is 1, so 2977 is not a divisor of 2978)
2978 / 2978 = 1 (the remainder is 0, so 2978 is a divisor of 2978)

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 2978 (i.e. 54.571054598569). 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 $\frac{N}{d} = D$ )

2978 / 1 = 2978 (the remainder is 0, so 1 and 2978 are divisors of 2978)
2978 / 2 = 1489 (the remainder is 0, so 2 and 1489 are divisors of 2978)
2978 / 3 = 992.66666666667 (the remainder is 2, so 3 is not a divisor of 2978)
...
2978 / 53 = 56.188679245283 (the remainder is 10, so 53 is not a divisor of 2978)
2978 / 54 = 55.148148148148 (the remainder is 8, so 54 is not a divisor of 2978)