11is an odd number,as it is not divisible by 2
The factors for 11 are all the numbers between -11 and 11 , which divide 11 without leaving any remainder. Since 11 divided by -11 is an integer, -11 is a factor of 11 .
Since 11 divided by -11 is a whole number, -11 is a factor of 11
Since 11 divided by -1 is a whole number, -1 is a factor of 11
Since 11 divided by 1 is a whole number, 1 is a factor of 11
Multiples of 11 are all integers divisible by 11 , i.e. the remainder of the full division by 11 is zero. There are infinite multiples of 11. The smallest multiples of 11 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 11 since 0 × 11 = 0
11 : in fact, 11 is a multiple of itself, since 11 is divisible by 11 (it was 11 / 11 = 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 11, the answer is: yes, 11 is a prime number because it only has two different divisors: 1 and itself (11).
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 11). 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 3.317 ). 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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