70001is an odd number,as it is not divisible by 2
The factors for 70001 are all the numbers between -70001 and 70001 , which divide 70001 without leaving any remainder. Since 70001 divided by -70001 is an integer, -70001 is a factor of 70001 .
Since 70001 divided by -70001 is a whole number, -70001 is a factor of 70001
Since 70001 divided by -1 is a whole number, -1 is a factor of 70001
Since 70001 divided by 1 is a whole number, 1 is a factor of 70001
Multiples of 70001 are all integers divisible by 70001 , i.e. the remainder of the full division by 70001 is zero. There are infinite multiples of 70001. The smallest multiples of 70001 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 70001 since 0 × 70001 = 0
70001 : in fact, 70001 is a multiple of itself, since 70001 is divisible by 70001 (it was 70001 / 70001 = 1, so the rest of this division is zero)
140002: in fact, 140002 = 70001 × 2
210003: in fact, 210003 = 70001 × 3
280004: in fact, 280004 = 70001 × 4
350005: in fact, 350005 = 70001 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 70001, the answer is: yes, 70001 is a prime number because it only has two different divisors: 1 and itself (70001).
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 70001). 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 264.577 ). 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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