42689is an odd number,as it is not divisible by 2
The factors for 42689 are all the numbers between -42689 and 42689 , which divide 42689 without leaving any remainder. Since 42689 divided by -42689 is an integer, -42689 is a factor of 42689 .
Since 42689 divided by -42689 is a whole number, -42689 is a factor of 42689
Since 42689 divided by -1 is a whole number, -1 is a factor of 42689
Since 42689 divided by 1 is a whole number, 1 is a factor of 42689
Multiples of 42689 are all integers divisible by 42689 , i.e. the remainder of the full division by 42689 is zero. There are infinite multiples of 42689. The smallest multiples of 42689 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 42689 since 0 × 42689 = 0
42689 : in fact, 42689 is a multiple of itself, since 42689 is divisible by 42689 (it was 42689 / 42689 = 1, so the rest of this division is zero)
85378: in fact, 85378 = 42689 × 2
128067: in fact, 128067 = 42689 × 3
170756: in fact, 170756 = 42689 × 4
213445: in fact, 213445 = 42689 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 42689, the answer is: yes, 42689 is a prime number because it only has two different divisors: 1 and itself (42689).
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 42689). 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 206.613 ). 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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