31321is an odd number,as it is not divisible by 2
The factors for 31321 are all the numbers between -31321 and 31321 , which divide 31321 without leaving any remainder. Since 31321 divided by -31321 is an integer, -31321 is a factor of 31321 .
Since 31321 divided by -31321 is a whole number, -31321 is a factor of 31321
Since 31321 divided by -1 is a whole number, -1 is a factor of 31321
Since 31321 divided by 1 is a whole number, 1 is a factor of 31321
Multiples of 31321 are all integers divisible by 31321 , i.e. the remainder of the full division by 31321 is zero. There are infinite multiples of 31321. The smallest multiples of 31321 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 31321 since 0 × 31321 = 0
31321 : in fact, 31321 is a multiple of itself, since 31321 is divisible by 31321 (it was 31321 / 31321 = 1, so the rest of this division is zero)
62642: in fact, 62642 = 31321 × 2
93963: in fact, 93963 = 31321 × 3
125284: in fact, 125284 = 31321 × 4
156605: in fact, 156605 = 31321 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 31321, the answer is: yes, 31321 is a prime number because it only has two different divisors: 1 and itself (31321).
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 31321). 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 176.977 ). 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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