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100501is an odd number,as it is not divisible by 2
The factors for 100501 are all the numbers between -100501 and 100501 , which divide 100501 without leaving any remainder. Since 100501 divided by -100501 is an integer, -100501 is a factor of 100501 .
Since 100501 divided by -100501 is a whole number, -100501 is a factor of 100501
Since 100501 divided by -1 is a whole number, -1 is a factor of 100501
Since 100501 divided by 1 is a whole number, 1 is a factor of 100501
Multiples of 100501 are all integers divisible by 100501 , i.e. the remainder of the full division by 100501 is zero. There are infinite multiples of 100501. The smallest multiples of 100501 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 100501 since 0 × 100501 = 0
100501 : in fact, 100501 is a multiple of itself, since 100501 is divisible by 100501 (it was 100501 / 100501 = 1, so the rest of this division is zero)
201002: in fact, 201002 = 100501 × 2
301503: in fact, 301503 = 100501 × 3
402004: in fact, 402004 = 100501 × 4
502505: in fact, 502505 = 100501 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 100501, the answer is: yes, 100501 is a prime number because it only has two different divisors: 1 and itself (100501).
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 100501). 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 317.019 ). 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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