32009is an odd number,as it is not divisible by 2
The factors for 32009 are all the numbers between -32009 and 32009 , which divide 32009 without leaving any remainder. Since 32009 divided by -32009 is an integer, -32009 is a factor of 32009 .
Since 32009 divided by -32009 is a whole number, -32009 is a factor of 32009
Since 32009 divided by -1 is a whole number, -1 is a factor of 32009
Since 32009 divided by 1 is a whole number, 1 is a factor of 32009
Multiples of 32009 are all integers divisible by 32009 , i.e. the remainder of the full division by 32009 is zero. There are infinite multiples of 32009. The smallest multiples of 32009 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 32009 since 0 × 32009 = 0
32009 : in fact, 32009 is a multiple of itself, since 32009 is divisible by 32009 (it was 32009 / 32009 = 1, so the rest of this division is zero)
64018: in fact, 64018 = 32009 × 2
96027: in fact, 96027 = 32009 × 3
128036: in fact, 128036 = 32009 × 4
160045: in fact, 160045 = 32009 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 32009, the answer is: yes, 32009 is a prime number because it only has two different divisors: 1 and itself (32009).
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 32009). 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 178.911 ). 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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