21997is an odd number,as it is not divisible by 2
The factors for 21997 are all the numbers between -21997 and 21997 , which divide 21997 without leaving any remainder. Since 21997 divided by -21997 is an integer, -21997 is a factor of 21997 .
Since 21997 divided by -21997 is a whole number, -21997 is a factor of 21997
Since 21997 divided by -1 is a whole number, -1 is a factor of 21997
Since 21997 divided by 1 is a whole number, 1 is a factor of 21997
Multiples of 21997 are all integers divisible by 21997 , i.e. the remainder of the full division by 21997 is zero. There are infinite multiples of 21997. The smallest multiples of 21997 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 21997 since 0 × 21997 = 0
21997 : in fact, 21997 is a multiple of itself, since 21997 is divisible by 21997 (it was 21997 / 21997 = 1, so the rest of this division is zero)
43994: in fact, 43994 = 21997 × 2
65991: in fact, 65991 = 21997 × 3
87988: in fact, 87988 = 21997 × 4
109985: in fact, 109985 = 21997 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 21997, the answer is: yes, 21997 is a prime number because it only has two different divisors: 1 and itself (21997).
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 21997). 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 148.314 ). 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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