9631is an odd number,as it is not divisible by 2
The factors for 9631 are all the numbers between -9631 and 9631 , which divide 9631 without leaving any remainder. Since 9631 divided by -9631 is an integer, -9631 is a factor of 9631 .
Since 9631 divided by -9631 is a whole number, -9631 is a factor of 9631
Since 9631 divided by -1 is a whole number, -1 is a factor of 9631
Since 9631 divided by 1 is a whole number, 1 is a factor of 9631
Multiples of 9631 are all integers divisible by 9631 , i.e. the remainder of the full division by 9631 is zero. There are infinite multiples of 9631. The smallest multiples of 9631 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9631 since 0 × 9631 = 0
9631 : in fact, 9631 is a multiple of itself, since 9631 is divisible by 9631 (it was 9631 / 9631 = 1, so the rest of this division is zero)
19262: in fact, 19262 = 9631 × 2
28893: in fact, 28893 = 9631 × 3
38524: in fact, 38524 = 9631 × 4
48155: in fact, 48155 = 9631 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9631, the answer is: yes, 9631 is a prime number because it only has two different divisors: 1 and itself (9631).
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 9631). 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 98.138 ). 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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