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6709is an odd number,as it is not divisible by 2
The factors for 6709 are all the numbers between -6709 and 6709 , which divide 6709 without leaving any remainder. Since 6709 divided by -6709 is an integer, -6709 is a factor of 6709 .
Since 6709 divided by -6709 is a whole number, -6709 is a factor of 6709
Since 6709 divided by -1 is a whole number, -1 is a factor of 6709
Since 6709 divided by 1 is a whole number, 1 is a factor of 6709
Multiples of 6709 are all integers divisible by 6709 , i.e. the remainder of the full division by 6709 is zero. There are infinite multiples of 6709. The smallest multiples of 6709 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 6709 since 0 × 6709 = 0
6709 : in fact, 6709 is a multiple of itself, since 6709 is divisible by 6709 (it was 6709 / 6709 = 1, so the rest of this division is zero)
13418: in fact, 13418 = 6709 × 2
20127: in fact, 20127 = 6709 × 3
26836: in fact, 26836 = 6709 × 4
33545: in fact, 33545 = 6709 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 6709, the answer is: yes, 6709 is a prime number because it only has two different divisors: 1 and itself (6709).
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 6709). 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 81.908 ). 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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