21221is an odd number,as it is not divisible by 2
The factors for 21221 are all the numbers between -21221 and 21221 , which divide 21221 without leaving any remainder. Since 21221 divided by -21221 is an integer, -21221 is a factor of 21221 .
Since 21221 divided by -21221 is a whole number, -21221 is a factor of 21221
Since 21221 divided by -1 is a whole number, -1 is a factor of 21221
Since 21221 divided by 1 is a whole number, 1 is a factor of 21221
Multiples of 21221 are all integers divisible by 21221 , i.e. the remainder of the full division by 21221 is zero. There are infinite multiples of 21221. The smallest multiples of 21221 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 21221 since 0 × 21221 = 0
21221 : in fact, 21221 is a multiple of itself, since 21221 is divisible by 21221 (it was 21221 / 21221 = 1, so the rest of this division is zero)
42442: in fact, 42442 = 21221 × 2
63663: in fact, 63663 = 21221 × 3
84884: in fact, 84884 = 21221 × 4
106105: in fact, 106105 = 21221 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 21221, the answer is: yes, 21221 is a prime number because it only has two different divisors: 1 and itself (21221).
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 21221). 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 145.674 ). 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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