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40213is an odd number,as it is not divisible by 2
The factors for 40213 are all the numbers between -40213 and 40213 , which divide 40213 without leaving any remainder. Since 40213 divided by -40213 is an integer, -40213 is a factor of 40213 .
Since 40213 divided by -40213 is a whole number, -40213 is a factor of 40213
Since 40213 divided by -1 is a whole number, -1 is a factor of 40213
Since 40213 divided by 1 is a whole number, 1 is a factor of 40213
Multiples of 40213 are all integers divisible by 40213 , i.e. the remainder of the full division by 40213 is zero. There are infinite multiples of 40213. The smallest multiples of 40213 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 40213 since 0 × 40213 = 0
40213 : in fact, 40213 is a multiple of itself, since 40213 is divisible by 40213 (it was 40213 / 40213 = 1, so the rest of this division is zero)
80426: in fact, 80426 = 40213 × 2
120639: in fact, 120639 = 40213 × 3
160852: in fact, 160852 = 40213 × 4
201065: in fact, 201065 = 40213 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 40213, the answer is: yes, 40213 is a prime number because it only has two different divisors: 1 and itself (40213).
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 40213). 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 200.532 ). 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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