102001is an odd number,as it is not divisible by 2
The factors for 102001 are all the numbers between -102001 and 102001 , which divide 102001 without leaving any remainder. Since 102001 divided by -102001 is an integer, -102001 is a factor of 102001 .
Since 102001 divided by -102001 is a whole number, -102001 is a factor of 102001
Since 102001 divided by -1 is a whole number, -1 is a factor of 102001
Since 102001 divided by 1 is a whole number, 1 is a factor of 102001
Multiples of 102001 are all integers divisible by 102001 , i.e. the remainder of the full division by 102001 is zero. There are infinite multiples of 102001. The smallest multiples of 102001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 102001 since 0 × 102001 = 0
102001 : in fact, 102001 is a multiple of itself, since 102001 is divisible by 102001 (it was 102001 / 102001 = 1, so the rest of this division is zero)
204002: in fact, 204002 = 102001 × 2
306003: in fact, 306003 = 102001 × 3
408004: in fact, 408004 = 102001 × 4
510005: in fact, 510005 = 102001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 102001, the answer is: yes, 102001 is a prime number because it only has two different divisors: 1 and itself (102001).
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 102001). 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 319.376 ). 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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