500009is an odd number,as it is not divisible by 2
The factors for 500009 are all the numbers between -500009 and 500009 , which divide 500009 without leaving any remainder. Since 500009 divided by -500009 is an integer, -500009 is a factor of 500009 .
Since 500009 divided by -500009 is a whole number, -500009 is a factor of 500009
Since 500009 divided by -1 is a whole number, -1 is a factor of 500009
Since 500009 divided by 1 is a whole number, 1 is a factor of 500009
Multiples of 500009 are all integers divisible by 500009 , i.e. the remainder of the full division by 500009 is zero. There are infinite multiples of 500009. The smallest multiples of 500009 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 500009 since 0 × 500009 = 0
500009 : in fact, 500009 is a multiple of itself, since 500009 is divisible by 500009 (it was 500009 / 500009 = 1, so the rest of this division is zero)
1000018: in fact, 1000018 = 500009 × 2
1500027: in fact, 1500027 = 500009 × 3
2000036: in fact, 2000036 = 500009 × 4
2500045: in fact, 2500045 = 500009 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 500009, the answer is: yes, 500009 is a prime number because it only has two different divisors: 1 and itself (500009).
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 500009). 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 707.113 ). 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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