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33997is an odd number,as it is not divisible by 2
The factors for 33997 are all the numbers between -33997 and 33997 , which divide 33997 without leaving any remainder. Since 33997 divided by -33997 is an integer, -33997 is a factor of 33997 .
Since 33997 divided by -33997 is a whole number, -33997 is a factor of 33997
Since 33997 divided by -1 is a whole number, -1 is a factor of 33997
Since 33997 divided by 1 is a whole number, 1 is a factor of 33997
Multiples of 33997 are all integers divisible by 33997 , i.e. the remainder of the full division by 33997 is zero. There are infinite multiples of 33997. The smallest multiples of 33997 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 33997 since 0 × 33997 = 0
33997 : in fact, 33997 is a multiple of itself, since 33997 is divisible by 33997 (it was 33997 / 33997 = 1, so the rest of this division is zero)
67994: in fact, 67994 = 33997 × 2
101991: in fact, 101991 = 33997 × 3
135988: in fact, 135988 = 33997 × 4
169985: in fact, 169985 = 33997 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 33997, the answer is: yes, 33997 is a prime number because it only has two different divisors: 1 and itself (33997).
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 33997). 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 184.383 ). 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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