72313is an odd number,as it is not divisible by 2
The factors for 72313 are all the numbers between -72313 and 72313 , which divide 72313 without leaving any remainder. Since 72313 divided by -72313 is an integer, -72313 is a factor of 72313 .
Since 72313 divided by -72313 is a whole number, -72313 is a factor of 72313
Since 72313 divided by -1 is a whole number, -1 is a factor of 72313
Since 72313 divided by 1 is a whole number, 1 is a factor of 72313
Multiples of 72313 are all integers divisible by 72313 , i.e. the remainder of the full division by 72313 is zero. There are infinite multiples of 72313. The smallest multiples of 72313 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 72313 since 0 × 72313 = 0
72313 : in fact, 72313 is a multiple of itself, since 72313 is divisible by 72313 (it was 72313 / 72313 = 1, so the rest of this division is zero)
144626: in fact, 144626 = 72313 × 2
216939: in fact, 216939 = 72313 × 3
289252: in fact, 289252 = 72313 × 4
361565: in fact, 361565 = 72313 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 72313, the answer is: yes, 72313 is a prime number because it only has two different divisors: 1 and itself (72313).
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 72313). 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 268.911 ). 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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