123001is an odd number,as it is not divisible by 2
The factors for 123001 are all the numbers between -123001 and 123001 , which divide 123001 without leaving any remainder. Since 123001 divided by -123001 is an integer, -123001 is a factor of 123001 .
Since 123001 divided by -123001 is a whole number, -123001 is a factor of 123001
Since 123001 divided by -1 is a whole number, -1 is a factor of 123001
Since 123001 divided by 1 is a whole number, 1 is a factor of 123001
Multiples of 123001 are all integers divisible by 123001 , i.e. the remainder of the full division by 123001 is zero. There are infinite multiples of 123001. The smallest multiples of 123001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 123001 since 0 × 123001 = 0
123001 : in fact, 123001 is a multiple of itself, since 123001 is divisible by 123001 (it was 123001 / 123001 = 1, so the rest of this division is zero)
246002: in fact, 246002 = 123001 × 2
369003: in fact, 369003 = 123001 × 3
492004: in fact, 492004 = 123001 × 4
615005: in fact, 615005 = 123001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 123001, the answer is: yes, 123001 is a prime number because it only has two different divisors: 1 and itself (123001).
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 123001). 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 350.715 ). 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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