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9901is an odd number,as it is not divisible by 2
The factors for 9901 are all the numbers between -9901 and 9901 , which divide 9901 without leaving any remainder. Since 9901 divided by -9901 is an integer, -9901 is a factor of 9901 .
Since 9901 divided by -9901 is a whole number, -9901 is a factor of 9901
Since 9901 divided by -1 is a whole number, -1 is a factor of 9901
Since 9901 divided by 1 is a whole number, 1 is a factor of 9901
Multiples of 9901 are all integers divisible by 9901 , i.e. the remainder of the full division by 9901 is zero. There are infinite multiples of 9901. The smallest multiples of 9901 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9901 since 0 × 9901 = 0
9901 : in fact, 9901 is a multiple of itself, since 9901 is divisible by 9901 (it was 9901 / 9901 = 1, so the rest of this division is zero)
19802: in fact, 19802 = 9901 × 2
29703: in fact, 29703 = 9901 × 3
39604: in fact, 39604 = 9901 × 4
49505: in fact, 49505 = 9901 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9901, the answer is: yes, 9901 is a prime number because it only has two different divisors: 1 and itself (9901).
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 9901). 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 99.504 ). 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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