40031is an odd number,as it is not divisible by 2
The factors for 40031 are all the numbers between -40031 and 40031 , which divide 40031 without leaving any remainder. Since 40031 divided by -40031 is an integer, -40031 is a factor of 40031 .
Since 40031 divided by -40031 is a whole number, -40031 is a factor of 40031
Since 40031 divided by -1 is a whole number, -1 is a factor of 40031
Since 40031 divided by 1 is a whole number, 1 is a factor of 40031
Multiples of 40031 are all integers divisible by 40031 , i.e. the remainder of the full division by 40031 is zero. There are infinite multiples of 40031. The smallest multiples of 40031 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 40031 since 0 × 40031 = 0
40031 : in fact, 40031 is a multiple of itself, since 40031 is divisible by 40031 (it was 40031 / 40031 = 1, so the rest of this division is zero)
80062: in fact, 80062 = 40031 × 2
120093: in fact, 120093 = 40031 × 3
160124: in fact, 160124 = 40031 × 4
200155: in fact, 200155 = 40031 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 40031, the answer is: yes, 40031 is a prime number because it only has two different divisors: 1 and itself (40031).
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 40031). 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 200.077 ). 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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