9689is an odd number,as it is not divisible by 2
The factors for 9689 are all the numbers between -9689 and 9689 , which divide 9689 without leaving any remainder. Since 9689 divided by -9689 is an integer, -9689 is a factor of 9689 .
Since 9689 divided by -9689 is a whole number, -9689 is a factor of 9689
Since 9689 divided by -1 is a whole number, -1 is a factor of 9689
Since 9689 divided by 1 is a whole number, 1 is a factor of 9689
Multiples of 9689 are all integers divisible by 9689 , i.e. the remainder of the full division by 9689 is zero. There are infinite multiples of 9689. The smallest multiples of 9689 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9689 since 0 × 9689 = 0
9689 : in fact, 9689 is a multiple of itself, since 9689 is divisible by 9689 (it was 9689 / 9689 = 1, so the rest of this division is zero)
19378: in fact, 19378 = 9689 × 2
29067: in fact, 29067 = 9689 × 3
38756: in fact, 38756 = 9689 × 4
48445: in fact, 48445 = 9689 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9689, the answer is: yes, 9689 is a prime number because it only has two different divisors: 1 and itself (9689).
To know the primality of an integer, we can use several algorithms. The most naive is to try all divisors below the number you want to know if it is prime (in our case 9689). We can already eliminate even numbers bigger than 2 (then 4 , 6 , 8 ...). Besides, we can stop at the square root of the number in question (here 98.433 ). Historically, the Eratosthenes screen (which dates back to Antiquity) uses this technique relatively effectively.
More modern techniques include the Atkin screen, probabilistic tests, or the cyclotomic test.
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