14009is an odd number,as it is not divisible by 2
The factors for 14009 are all the numbers between -14009 and 14009 , which divide 14009 without leaving any remainder. Since 14009 divided by -14009 is an integer, -14009 is a factor of 14009 .
Since 14009 divided by -14009 is a whole number, -14009 is a factor of 14009
Since 14009 divided by -1 is a whole number, -1 is a factor of 14009
Since 14009 divided by 1 is a whole number, 1 is a factor of 14009
Multiples of 14009 are all integers divisible by 14009 , i.e. the remainder of the full division by 14009 is zero. There are infinite multiples of 14009. The smallest multiples of 14009 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 14009 since 0 × 14009 = 0
14009 : in fact, 14009 is a multiple of itself, since 14009 is divisible by 14009 (it was 14009 / 14009 = 1, so the rest of this division is zero)
28018: in fact, 28018 = 14009 × 2
42027: in fact, 42027 = 14009 × 3
56036: in fact, 56036 = 14009 × 4
70045: in fact, 70045 = 14009 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 14009, the answer is: yes, 14009 is a prime number because it only has two different divisors: 1 and itself (14009).
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 14009). 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 118.36 ). 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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