21001is an odd number,as it is not divisible by 2
The factors for 21001 are all the numbers between -21001 and 21001 , which divide 21001 without leaving any remainder. Since 21001 divided by -21001 is an integer, -21001 is a factor of 21001 .
Since 21001 divided by -21001 is a whole number, -21001 is a factor of 21001
Since 21001 divided by -1 is a whole number, -1 is a factor of 21001
Since 21001 divided by 1 is a whole number, 1 is a factor of 21001
Multiples of 21001 are all integers divisible by 21001 , i.e. the remainder of the full division by 21001 is zero. There are infinite multiples of 21001. The smallest multiples of 21001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 21001 since 0 × 21001 = 0
21001 : in fact, 21001 is a multiple of itself, since 21001 is divisible by 21001 (it was 21001 / 21001 = 1, so the rest of this division is zero)
42002: in fact, 42002 = 21001 × 2
63003: in fact, 63003 = 21001 × 3
84004: in fact, 84004 = 21001 × 4
105005: in fact, 105005 = 21001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 21001, the answer is: yes, 21001 is a prime number because it only has two different divisors: 1 and itself (21001).
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 21001). 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 144.917 ). 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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