What are the divisors of 977?

1, 977

There is a total of 2 positive divisors.
The sum of these divisors is 978.
The arithmetic mean is 489.

2 odd divisors

1, 977

How to compute the divisors of 977?

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 977 by each of the numbers from 1 to 977 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)

977 / 1 = 977 (the remainder is 0, so 1 is a divisor of 977)
977 / 2 = 488.5 (the remainder is 1, so 2 is not a divisor of 977)
977 / 3 = 325.66666666667 (the remainder is 2, so 3 is not a divisor of 977)
...
977 / 976 = 1.0010245901639 (the remainder is 1, so 976 is not a divisor of 977)
977 / 977 = 1 (the remainder is 0, so 977 is a divisor of 977)

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 977 (i.e. 31.256999216176). 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 $\frac{N}{d} = D$ )

977 / 1 = 977 (the remainder is 0, so 1 and 977 are divisors of 977)
977 / 2 = 488.5 (the remainder is 1, so 2 is not a divisor of 977)
977 / 3 = 325.66666666667 (the remainder is 2, so 3 is not a divisor of 977)
...
977 / 30 = 32.566666666667 (the remainder is 17, so 30 is not a divisor of 977)
977 / 31 = 31.516129032258 (the remainder is 16, so 31 is not a divisor of 977)