9701is an odd number,as it is not divisible by 2
The factors for 9701 are all the numbers between -9701 and 9701 , which divide 9701 without leaving any remainder. Since 9701 divided by -9701 is an integer, -9701 is a factor of 9701 .
Since 9701 divided by -9701 is a whole number, -9701 is a factor of 9701
Since 9701 divided by -109 is a whole number, -109 is a factor of 9701
Since 9701 divided by -89 is a whole number, -89 is a factor of 9701
Since 9701 divided by -1 is a whole number, -1 is a factor of 9701
Since 9701 divided by 1 is a whole number, 1 is a factor of 9701
Since 9701 divided by 89 is a whole number, 89 is a factor of 9701
Since 9701 divided by 109 is a whole number, 109 is a factor of 9701
Multiples of 9701 are all integers divisible by 9701 , i.e. the remainder of the full division by 9701 is zero. There are infinite multiples of 9701. The smallest multiples of 9701 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 9701 since 0 × 9701 = 0
9701 : in fact, 9701 is a multiple of itself, since 9701 is divisible by 9701 (it was 9701 / 9701 = 1, so the rest of this division is zero)
19402: in fact, 19402 = 9701 × 2
29103: in fact, 29103 = 9701 × 3
38804: in fact, 38804 = 9701 × 4
48505: in fact, 48505 = 9701 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 9701, the answer is: No, 9701 is not a prime number.
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 9701). 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 98.494 ). 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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