42307is an odd number,as it is not divisible by 2
The factors for 42307 are all the numbers between -42307 and 42307 , which divide 42307 without leaving any remainder. Since 42307 divided by -42307 is an integer, -42307 is a factor of 42307 .
Since 42307 divided by -42307 is a whole number, -42307 is a factor of 42307
Since 42307 divided by -1 is a whole number, -1 is a factor of 42307
Since 42307 divided by 1 is a whole number, 1 is a factor of 42307
Multiples of 42307 are all integers divisible by 42307 , i.e. the remainder of the full division by 42307 is zero. There are infinite multiples of 42307. The smallest multiples of 42307 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 42307 since 0 × 42307 = 0
42307 : in fact, 42307 is a multiple of itself, since 42307 is divisible by 42307 (it was 42307 / 42307 = 1, so the rest of this division is zero)
84614: in fact, 84614 = 42307 × 2
126921: in fact, 126921 = 42307 × 3
169228: in fact, 169228 = 42307 × 4
211535: in fact, 211535 = 42307 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 42307, the answer is: yes, 42307 is a prime number because it only has two different divisors: 1 and itself (42307).
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 42307). 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 205.687 ). 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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