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21701is an odd number,as it is not divisible by 2
The factors for 21701 are all the numbers between -21701 and 21701 , which divide 21701 without leaving any remainder. Since 21701 divided by -21701 is an integer, -21701 is a factor of 21701 .
Since 21701 divided by -21701 is a whole number, -21701 is a factor of 21701
Since 21701 divided by -1 is a whole number, -1 is a factor of 21701
Since 21701 divided by 1 is a whole number, 1 is a factor of 21701
Multiples of 21701 are all integers divisible by 21701 , i.e. the remainder of the full division by 21701 is zero. There are infinite multiples of 21701. The smallest multiples of 21701 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 21701 since 0 × 21701 = 0
21701 : in fact, 21701 is a multiple of itself, since 21701 is divisible by 21701 (it was 21701 / 21701 = 1, so the rest of this division is zero)
43402: in fact, 43402 = 21701 × 2
65103: in fact, 65103 = 21701 × 3
86804: in fact, 86804 = 21701 × 4
108505: in fact, 108505 = 21701 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 21701, the answer is: yes, 21701 is a prime number because it only has two different divisors: 1 and itself (21701).
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 21701). 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 147.313 ). 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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