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20717is an odd number,as it is not divisible by 2
The factors for 20717 are all the numbers between -20717 and 20717 , which divide 20717 without leaving any remainder. Since 20717 divided by -20717 is an integer, -20717 is a factor of 20717 .
Since 20717 divided by -20717 is a whole number, -20717 is a factor of 20717
Since 20717 divided by -1 is a whole number, -1 is a factor of 20717
Since 20717 divided by 1 is a whole number, 1 is a factor of 20717
Multiples of 20717 are all integers divisible by 20717 , i.e. the remainder of the full division by 20717 is zero. There are infinite multiples of 20717. The smallest multiples of 20717 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 20717 since 0 × 20717 = 0
20717 : in fact, 20717 is a multiple of itself, since 20717 is divisible by 20717 (it was 20717 / 20717 = 1, so the rest of this division is zero)
41434: in fact, 41434 = 20717 × 2
62151: in fact, 62151 = 20717 × 3
82868: in fact, 82868 = 20717 × 4
103585: in fact, 103585 = 20717 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 20717, the answer is: yes, 20717 is a prime number because it only has two different divisors: 1 and itself (20717).
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 20717). 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 143.934 ). 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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