2017is an odd number,as it is not divisible by 2
The factors for 2017 are all the numbers between -2017 and 2017 , which divide 2017 without leaving any remainder. Since 2017 divided by -2017 is an integer, -2017 is a factor of 2017 .
Since 2017 divided by -2017 is a whole number, -2017 is a factor of 2017
Since 2017 divided by -1 is a whole number, -1 is a factor of 2017
Multiples of 2017 are all integers divisible by 2017 , i.e. the remainder of the full division by 2017 is zero. There are infinite multiples of 2017. The smallest multiples of 2017 are:
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 2017, the answer is: yes, 2017 is a prime number because it only has two different divisors: 1 and itself (2017).
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 2017). 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 44.911 ). 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: 2011
Next prime number: 2027