16007is an odd number,as it is not divisible by 2
The factors for 16007 are all the numbers between -16007 and 16007 , which divide 16007 without leaving any remainder. Since 16007 divided by -16007 is an integer, -16007 is a factor of 16007 .
Since 16007 divided by -16007 is a whole number, -16007 is a factor of 16007
Since 16007 divided by -1 is a whole number, -1 is a factor of 16007
Since 16007 divided by 1 is a whole number, 1 is a factor of 16007
Multiples of 16007 are all integers divisible by 16007 , i.e. the remainder of the full division by 16007 is zero. There are infinite multiples of 16007. The smallest multiples of 16007 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 16007 since 0 × 16007 = 0
16007 : in fact, 16007 is a multiple of itself, since 16007 is divisible by 16007 (it was 16007 / 16007 = 1, so the rest of this division is zero)
32014: in fact, 32014 = 16007 × 2
48021: in fact, 48021 = 16007 × 3
64028: in fact, 64028 = 16007 × 4
80035: in fact, 80035 = 16007 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 16007, the answer is: yes, 16007 is a prime number because it only has two different divisors: 1 and itself (16007).
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 16007). 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 126.519 ). 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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