17011is an odd number,as it is not divisible by 2
The factors for 17011 are all the numbers between -17011 and 17011 , which divide 17011 without leaving any remainder. Since 17011 divided by -17011 is an integer, -17011 is a factor of 17011 .
Since 17011 divided by -17011 is a whole number, -17011 is a factor of 17011
Since 17011 divided by -1 is a whole number, -1 is a factor of 17011
Since 17011 divided by 1 is a whole number, 1 is a factor of 17011
Multiples of 17011 are all integers divisible by 17011 , i.e. the remainder of the full division by 17011 is zero. There are infinite multiples of 17011. The smallest multiples of 17011 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 17011 since 0 × 17011 = 0
17011 : in fact, 17011 is a multiple of itself, since 17011 is divisible by 17011 (it was 17011 / 17011 = 1, so the rest of this division is zero)
34022: in fact, 34022 = 17011 × 2
51033: in fact, 51033 = 17011 × 3
68044: in fact, 68044 = 17011 × 4
85055: in fact, 85055 = 17011 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 17011, the answer is: yes, 17011 is a prime number because it only has two different divisors: 1 and itself (17011).
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 17011). 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 130.426 ). 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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