89is an odd number,as it is not divisible by 2
The factors for 89 are all the numbers between -89 and 89 , which divide 89 without leaving any remainder. Since 89 divided by -89 is an integer, -89 is a factor of 89 .
Since 89 divided by -89 is a whole number, -89 is a factor of 89
Since 89 divided by -1 is a whole number, -1 is a factor of 89
Since 89 divided by 1 is a whole number, 1 is a factor of 89
Multiples of 89 are all integers divisible by 89 , i.e. the remainder of the full division by 89 is zero. There are infinite multiples of 89. The smallest multiples of 89 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 89 since 0 × 89 = 0
89 : in fact, 89 is a multiple of itself, since 89 is divisible by 89 (it was 89 / 89 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 89, the answer is: yes, 89 is a prime number because it only has two different divisors: 1 and itself (89).
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 89). 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 9.434 ). 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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