123121is an odd number,as it is not divisible by 2
The factors for 123121 are all the numbers between -123121 and 123121 , which divide 123121 without leaving any remainder. Since 123121 divided by -123121 is an integer, -123121 is a factor of 123121 .
Since 123121 divided by -123121 is a whole number, -123121 is a factor of 123121
Since 123121 divided by -1 is a whole number, -1 is a factor of 123121
Since 123121 divided by 1 is a whole number, 1 is a factor of 123121
Multiples of 123121 are all integers divisible by 123121 , i.e. the remainder of the full division by 123121 is zero. There are infinite multiples of 123121. The smallest multiples of 123121 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 123121 since 0 × 123121 = 0
123121 : in fact, 123121 is a multiple of itself, since 123121 is divisible by 123121 (it was 123121 / 123121 = 1, so the rest of this division is zero)
246242: in fact, 246242 = 123121 × 2
369363: in fact, 369363 = 123121 × 3
492484: in fact, 492484 = 123121 × 4
615605: in fact, 615605 = 123121 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 123121, the answer is: yes, 123121 is a prime number because it only has two different divisors: 1 and itself (123121).
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 123121). 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 350.886 ). 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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