42397is an odd number,as it is not divisible by 2
The factors for 42397 are all the numbers between -42397 and 42397 , which divide 42397 without leaving any remainder. Since 42397 divided by -42397 is an integer, -42397 is a factor of 42397 .
Since 42397 divided by -42397 is a whole number, -42397 is a factor of 42397
Since 42397 divided by -1 is a whole number, -1 is a factor of 42397
Since 42397 divided by 1 is a whole number, 1 is a factor of 42397
Multiples of 42397 are all integers divisible by 42397 , i.e. the remainder of the full division by 42397 is zero. There are infinite multiples of 42397. The smallest multiples of 42397 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 42397 since 0 × 42397 = 0
42397 : in fact, 42397 is a multiple of itself, since 42397 is divisible by 42397 (it was 42397 / 42397 = 1, so the rest of this division is zero)
84794: in fact, 84794 = 42397 × 2
127191: in fact, 127191 = 42397 × 3
169588: in fact, 169588 = 42397 × 4
211985: in fact, 211985 = 42397 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 42397, the answer is: yes, 42397 is a prime number because it only has two different divisors: 1 and itself (42397).
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 42397). 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 205.905 ). 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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