31is an odd number,as it is not divisible by 2
The factors for 31 are all the numbers between -31 and 31 , which divide 31 without leaving any remainder. Since 31 divided by -31 is an integer, -31 is a factor of 31 .
Since 31 divided by -31 is a whole number, -31 is a factor of 31
Since 31 divided by -1 is a whole number, -1 is a factor of 31
Since 31 divided by 1 is a whole number, 1 is a factor of 31
Multiples of 31 are all integers divisible by 31 , i.e. the remainder of the full division by 31 is zero. There are infinite multiples of 31. The smallest multiples of 31 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 31 since 0 × 31 = 0
31 : in fact, 31 is a multiple of itself, since 31 is divisible by 31 (it was 31 / 31 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 31, the answer is: yes, 31 is a prime number because it only has two different divisors: 1 and itself (31).
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 31). 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 5.568 ). 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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