409is an odd number,as it is not divisible by 2
The factors for 409 are all the numbers between -409 and 409 , which divide 409 without leaving any remainder. Since 409 divided by -409 is an integer, -409 is a factor of 409 .
Since 409 divided by -409 is a whole number, -409 is a factor of 409
Since 409 divided by -1 is a whole number, -1 is a factor of 409
Multiples of 409 are all integers divisible by 409 , i.e. the remainder of the full division by 409 is zero. There are infinite multiples of 409. The smallest multiples of 409 are:
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 409, the answer is: yes, 409 is a prime number because it only has two different divisors: 1 and itself (409).
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 409). 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 20.224 ). 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.
Previous prime number: 401
Next prime number: 419