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200009is an odd number,as it is not divisible by 2
The factors for 200009 are all the numbers between -200009 and 200009 , which divide 200009 without leaving any remainder. Since 200009 divided by -200009 is an integer, -200009 is a factor of 200009 .
Since 200009 divided by -200009 is a whole number, -200009 is a factor of 200009
Since 200009 divided by -1 is a whole number, -1 is a factor of 200009
Since 200009 divided by 1 is a whole number, 1 is a factor of 200009
Multiples of 200009 are all integers divisible by 200009 , i.e. the remainder of the full division by 200009 is zero. There are infinite multiples of 200009. The smallest multiples of 200009 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 200009 since 0 × 200009 = 0
200009 : in fact, 200009 is a multiple of itself, since 200009 is divisible by 200009 (it was 200009 / 200009 = 1, so the rest of this division is zero)
400018: in fact, 400018 = 200009 × 2
600027: in fact, 600027 = 200009 × 3
800036: in fact, 800036 = 200009 × 4
1000045: in fact, 1000045 = 200009 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 200009, the answer is: yes, 200009 is a prime number because it only has two different divisors: 1 and itself (200009).
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 200009). 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 447.224 ). 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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