9001is an odd number,as it is not divisible by 2
The factors for 9001 are all the numbers between -9001 and 9001 , which divide 9001 without leaving any remainder. Since 9001 divided by -9001 is an integer, -9001 is a factor of 9001 .
Since 9001 divided by -9001 is a whole number, -9001 is a factor of 9001
Since 9001 divided by -1 is a whole number, -1 is a factor of 9001
Since 9001 divided by 1 is a whole number, 1 is a factor of 9001
Multiples of 9001 are all integers divisible by 9001 , i.e. the remainder of the full division by 9001 is zero. There are infinite multiples of 9001. The smallest multiples of 9001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9001 since 0 × 9001 = 0
9001 : in fact, 9001 is a multiple of itself, since 9001 is divisible by 9001 (it was 9001 / 9001 = 1, so the rest of this division is zero)
18002: in fact, 18002 = 9001 × 2
27003: in fact, 27003 = 9001 × 3
36004: in fact, 36004 = 9001 × 4
45005: in fact, 45005 = 9001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9001, the answer is: yes, 9001 is a prime number because it only has two different divisors: 1 and itself (9001).
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 9001). 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 94.874 ). 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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