17is an odd number,as it is not divisible by 2
The factors for 17 are all the numbers between -17 and 17 , which divide 17 without leaving any remainder. Since 17 divided by -17 is an integer, -17 is a factor of 17 .
Since 17 divided by -17 is a whole number, -17 is a factor of 17
Since 17 divided by -1 is a whole number, -1 is a factor of 17
Since 17 divided by 1 is a whole number, 1 is a factor of 17
Multiples of 17 are all integers divisible by 17 , i.e. the remainder of the full division by 17 is zero. There are infinite multiples of 17. The smallest multiples of 17 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 17 since 0 × 17 = 0
17 : in fact, 17 is a multiple of itself, since 17 is divisible by 17 (it was 17 / 17 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 17, the answer is: yes, 17 is a prime number because it only has two different divisors: 1 and itself (17).
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 17). 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 4.123 ). 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.
Previous prime number: 13
Next prime number: 19