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9677is an odd number,as it is not divisible by 2
The factors for 9677 are all the numbers between -9677 and 9677 , which divide 9677 without leaving any remainder. Since 9677 divided by -9677 is an integer, -9677 is a factor of 9677 .
Since 9677 divided by -9677 is a whole number, -9677 is a factor of 9677
Since 9677 divided by -1 is a whole number, -1 is a factor of 9677
Since 9677 divided by 1 is a whole number, 1 is a factor of 9677
Multiples of 9677 are all integers divisible by 9677 , i.e. the remainder of the full division by 9677 is zero. There are infinite multiples of 9677. The smallest multiples of 9677 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9677 since 0 × 9677 = 0
9677 : in fact, 9677 is a multiple of itself, since 9677 is divisible by 9677 (it was 9677 / 9677 = 1, so the rest of this division is zero)
19354: in fact, 19354 = 9677 × 2
29031: in fact, 29031 = 9677 × 3
38708: in fact, 38708 = 9677 × 4
48385: in fact, 48385 = 9677 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9677, the answer is: yes, 9677 is a prime number because it only has two different divisors: 1 and itself (9677).
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 9677). 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 98.372 ). 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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