401is an odd number,as it is not divisible by 2
The factors for 401 are all the numbers between -401 and 401 , which divide 401 without leaving any remainder. Since 401 divided by -401 is an integer, -401 is a factor of 401 .
Since 401 divided by -401 is a whole number, -401 is a factor of 401
Since 401 divided by -1 is a whole number, -1 is a factor of 401
Since 401 divided by 1 is a whole number, 1 is a factor of 401
Multiples of 401 are all integers divisible by 401 , i.e. the remainder of the full division by 401 is zero. There are infinite multiples of 401. The smallest multiples of 401 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 401 since 0 × 401 = 0
401 : in fact, 401 is a multiple of itself, since 401 is divisible by 401 (it was 401 / 401 = 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 401, the answer is: yes, 401 is a prime number because it only has two different divisors: 1 and itself (401).
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 401). 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 20.025 ). 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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