What are the divisors of 674?
1, 2, 337, 674
- There is a total of 4 positive divisors.
- The sum of these divisors is 1014.
- The arithmetic mean is 253.5.
2 even divisors
2, 674
2 odd divisors
1, 337
How to compute the divisors of 674?
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.
Brute force algorithm
We could start by using a brute-force method which would involve dividing 674 by each of the numbers from 1 to 674 to determine which ones have a remainder equal to 0.
(where is the integer part of the quotient)
- 674 / 1 = 674 (the remainder is 0, so 1 is a divisor of 674)
- 674 / 2 = 337 (the remainder is 0, so 2 is a divisor of 674)
- 674 / 3 = 224.66666666667 (the remainder is 2, so 3 is not a divisor of 674)
- ...
- 674 / 673 = 1.001485884101 (the remainder is 1, so 673 is not a divisor of 674)
- 674 / 674 = 1 (the remainder is 0, so 674 is a divisor of 674)
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 674 (i.e. 25.961509971494). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:
(thus, if , then )
- 674 / 1 = 674 (the remainder is 0, so 1 and 674 are divisors of 674)
- 674 / 2 = 337 (the remainder is 0, so 2 and 337 are divisors of 674)
- 674 / 3 = 224.66666666667 (the remainder is 2, so 3 is not a divisor of 674)
- ...
- 674 / 24 = 28.083333333333 (the remainder is 2, so 24 is not a divisor of 674)
- 674 / 25 = 26.96 (the remainder is 24, so 25 is not a divisor of 674)