32771is an odd number,as it is not divisible by 2
The factors for 32771 are all the numbers between -32771 and 32771 , which divide 32771 without leaving any remainder. Since 32771 divided by -32771 is an integer, -32771 is a factor of 32771 .
Since 32771 divided by -32771 is a whole number, -32771 is a factor of 32771
Since 32771 divided by -1 is a whole number, -1 is a factor of 32771
Since 32771 divided by 1 is a whole number, 1 is a factor of 32771
Multiples of 32771 are all integers divisible by 32771 , i.e. the remainder of the full division by 32771 is zero. There are infinite multiples of 32771. The smallest multiples of 32771 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 32771 since 0 × 32771 = 0
32771 : in fact, 32771 is a multiple of itself, since 32771 is divisible by 32771 (it was 32771 / 32771 = 1, so the rest of this division is zero)
65542: in fact, 65542 = 32771 × 2
98313: in fact, 98313 = 32771 × 3
131084: in fact, 131084 = 32771 × 4
163855: in fact, 163855 = 32771 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 32771, the answer is: yes, 32771 is a prime number because it only has two different divisors: 1 and itself (32771).
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 32771). 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 181.028 ). 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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