7013is an odd number,as it is not divisible by 2
The factors for 7013 are all the numbers between -7013 and 7013 , which divide 7013 without leaving any remainder. Since 7013 divided by -7013 is an integer, -7013 is a factor of 7013 .
Since 7013 divided by -7013 is a whole number, -7013 is a factor of 7013
Since 7013 divided by -1 is a whole number, -1 is a factor of 7013
Since 7013 divided by 1 is a whole number, 1 is a factor of 7013
Multiples of 7013 are all integers divisible by 7013 , i.e. the remainder of the full division by 7013 is zero. There are infinite multiples of 7013. The smallest multiples of 7013 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 7013 since 0 × 7013 = 0
7013 : in fact, 7013 is a multiple of itself, since 7013 is divisible by 7013 (it was 7013 / 7013 = 1, so the rest of this division is zero)
14026: in fact, 14026 = 7013 × 2
21039: in fact, 21039 = 7013 × 3
28052: in fact, 28052 = 7013 × 4
35065: in fact, 35065 = 7013 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 7013, the answer is: yes, 7013 is a prime number because it only has two different divisors: 1 and itself (7013).
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 7013). 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 83.744 ). 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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