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In addition we can say of the number **406 that it is even**

406 is an even number, as it is divisible by 2 : 406/2 = 203

The factors for 406 are all the numbers between -406 and 406 , which divide 406 without leaving any remainder. Since 406 divided by -406 is an integer, -406 is a factor of 406 .

Since 406 divided by -406 is a whole number, -406 is a factor of 406

Since 406 divided by -203 is a whole number, -203 is a factor of 406

Since 406 divided by -58 is a whole number, -58 is a factor of 406

Since 406 divided by -29 is a whole number, -29 is a factor of 406

Since 406 divided by -14 is a whole number, -14 is a factor of 406

Since 406 divided by -7 is a whole number, -7 is a factor of 406

Since 406 divided by -2 is a whole number, -2 is a factor of 406

Since 406 divided by -1 is a whole number, -1 is a factor of 406

Since 406 divided by 1 is a whole number, 1 is a factor of 406

Since 406 divided by 2 is a whole number, 2 is a factor of 406

Since 406 divided by 7 is a whole number, 7 is a factor of 406

Since 406 divided by 14 is a whole number, 14 is a factor of 406

Since 406 divided by 29 is a whole number, 29 is a factor of 406

Since 406 divided by 58 is a whole number, 58 is a factor of 406

Since 406 divided by 203 is a whole number, 203 is a factor of 406

Multiples of 406 are all integers divisible by 406 , i.e. the remainder of the full division by 406 is zero. There are infinite multiples of 406. The smallest multiples of 406 are:

0 : in fact, 0 is divisible by any integer, so it is also a multiple of 406 since 0 × 406 = 0

406 : in fact, 406 is a multiple of itself, since 406 is divisible by 406 (it was 406 / 406 = 1, so the rest of this division is zero)

etc.

It is possible to determine using mathematical techniques whether an integer is prime or not.

for 406, the answer is:
**No, 406 is not a prime number**.

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 406). 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 20.149 ). 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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Next prime number: 409

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