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601is an odd number,as it is not divisible by 2
The factors for 601 are all the numbers between -601 and 601 , which divide 601 without leaving any remainder. Since 601 divided by -601 is an integer, -601 is a factor of 601 .
Since 601 divided by -601 is a whole number, -601 is a factor of 601
Since 601 divided by -1 is a whole number, -1 is a factor of 601
Since 601 divided by 1 is a whole number, 1 is a factor of 601
Multiples of 601 are all integers divisible by 601 , i.e. the remainder of the full division by 601 is zero. There are infinite multiples of 601. The smallest multiples of 601 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 601 since 0 × 601 = 0
601 : in fact, 601 is a multiple of itself, since 601 is divisible by 601 (it was 601 / 601 = 1, so the rest of this division is zero)
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 601, the answer is: yes, 601 is a prime number because it only has two different divisors: 1 and itself (601).
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 601). 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 24.515 ). 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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