72701is an odd number,as it is not divisible by 2
The factors for 72701 are all the numbers between -72701 and 72701 , which divide 72701 without leaving any remainder. Since 72701 divided by -72701 is an integer, -72701 is a factor of 72701 .
Since 72701 divided by -72701 is a whole number, -72701 is a factor of 72701
Since 72701 divided by -1 is a whole number, -1 is a factor of 72701
Since 72701 divided by 1 is a whole number, 1 is a factor of 72701
Multiples of 72701 are all integers divisible by 72701 , i.e. the remainder of the full division by 72701 is zero. There are infinite multiples of 72701. The smallest multiples of 72701 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 72701 since 0 × 72701 = 0
72701 : in fact, 72701 is a multiple of itself, since 72701 is divisible by 72701 (it was 72701 / 72701 = 1, so the rest of this division is zero)
145402: in fact, 145402 = 72701 × 2
218103: in fact, 218103 = 72701 × 3
290804: in fact, 290804 = 72701 × 4
363505: in fact, 363505 = 72701 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 72701, the answer is: yes, 72701 is a prime number because it only has two different divisors: 1 and itself (72701).
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 72701). 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 269.631 ). 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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