38501is an odd number,as it is not divisible by 2
The factors for 38501 are all the numbers between -38501 and 38501 , which divide 38501 without leaving any remainder. Since 38501 divided by -38501 is an integer, -38501 is a factor of 38501 .
Since 38501 divided by -38501 is a whole number, -38501 is a factor of 38501
Since 38501 divided by -1 is a whole number, -1 is a factor of 38501
Since 38501 divided by 1 is a whole number, 1 is a factor of 38501
Multiples of 38501 are all integers divisible by 38501 , i.e. the remainder of the full division by 38501 is zero. There are infinite multiples of 38501. The smallest multiples of 38501 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 38501 since 0 × 38501 = 0
38501 : in fact, 38501 is a multiple of itself, since 38501 is divisible by 38501 (it was 38501 / 38501 = 1, so the rest of this division is zero)
77002: in fact, 77002 = 38501 × 2
115503: in fact, 115503 = 38501 × 3
154004: in fact, 154004 = 38501 × 4
192505: in fact, 192505 = 38501 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 38501, the answer is: yes, 38501 is a prime number because it only has two different divisors: 1 and itself (38501).
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 38501). 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 196.217 ). 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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