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521is an odd number,as it is not divisible by 2
The factors for 521 are all the numbers between -521 and 521 , which divide 521 without leaving any remainder. Since 521 divided by -521 is an integer, -521 is a factor of 521 .
Since 521 divided by -521 is a whole number, -521 is a factor of 521
Since 521 divided by -1 is a whole number, -1 is a factor of 521
Since 521 divided by 1 is a whole number, 1 is a factor of 521
Multiples of 521 are all integers divisible by 521 , i.e. the remainder of the full division by 521 is zero. There are infinite multiples of 521. The smallest multiples of 521 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 521 since 0 × 521 = 0
521 : in fact, 521 is a multiple of itself, since 521 is divisible by 521 (it was 521 / 521 = 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 521, the answer is: yes, 521 is a prime number because it only has two different divisors: 1 and itself (521).
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 521). 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 22.825 ). 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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