197is an odd number,as it is not divisible by 2
The factors for 197 are all the numbers between -197 and 197 , which divide 197 without leaving any remainder. Since 197 divided by -197 is an integer, -197 is a factor of 197 .
Since 197 divided by -197 is a whole number, -197 is a factor of 197
Since 197 divided by -1 is a whole number, -1 is a factor of 197
Since 197 divided by 1 is a whole number, 1 is a factor of 197
Multiples of 197 are all integers divisible by 197 , i.e. the remainder of the full division by 197 is zero. There are infinite multiples of 197. The smallest multiples of 197 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 197 since 0 × 197 = 0
197 : in fact, 197 is a multiple of itself, since 197 is divisible by 197 (it was 197 / 197 = 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 197, the answer is: yes, 197 is a prime number because it only has two different divisors: 1 and itself (197).
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 197). 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 14.036 ). 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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