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21397is an odd number,as it is not divisible by 2
The factors for 21397 are all the numbers between -21397 and 21397 , which divide 21397 without leaving any remainder. Since 21397 divided by -21397 is an integer, -21397 is a factor of 21397 .
Since 21397 divided by -21397 is a whole number, -21397 is a factor of 21397
Since 21397 divided by -1 is a whole number, -1 is a factor of 21397
Since 21397 divided by 1 is a whole number, 1 is a factor of 21397
Multiples of 21397 are all integers divisible by 21397 , i.e. the remainder of the full division by 21397 is zero. There are infinite multiples of 21397. The smallest multiples of 21397 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 21397 since 0 × 21397 = 0
21397 : in fact, 21397 is a multiple of itself, since 21397 is divisible by 21397 (it was 21397 / 21397 = 1, so the rest of this division is zero)
42794: in fact, 42794 = 21397 × 2
64191: in fact, 64191 = 21397 × 3
85588: in fact, 85588 = 21397 × 4
106985: in fact, 106985 = 21397 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 21397, the answer is: yes, 21397 is a prime number because it only has two different divisors: 1 and itself (21397).
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 21397). 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 146.277 ). 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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