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1999is an odd number,as it is not divisible by 2
The factors for 1999 are all the numbers between -1999 and 1999 , which divide 1999 without leaving any remainder. Since 1999 divided by -1999 is an integer, -1999 is a factor of 1999 .
Since 1999 divided by -1999 is a whole number, -1999 is a factor of 1999
Since 1999 divided by -1 is a whole number, -1 is a factor of 1999
Since 1999 divided by 1 is a whole number, 1 is a factor of 1999
Multiples of 1999 are all integers divisible by 1999 , i.e. the remainder of the full division by 1999 is zero. There are infinite multiples of 1999. The smallest multiples of 1999 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 1999 since 0 × 1999 = 0
1999 : in fact, 1999 is a multiple of itself, since 1999 is divisible by 1999 (it was 1999 / 1999 = 1, so the rest of this division is zero)
3998: in fact, 3998 = 1999 × 2
5997: in fact, 5997 = 1999 × 3
7996: in fact, 7996 = 1999 × 4
9995: in fact, 9995 = 1999 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 1999, the answer is: yes, 1999 is a prime number because it only has two different divisors: 1 and itself (1999).
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 1999). 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 44.71 ). 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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