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42767is an odd number,as it is not divisible by 2
The factors for 42767 are all the numbers between -42767 and 42767 , which divide 42767 without leaving any remainder. Since 42767 divided by -42767 is an integer, -42767 is a factor of 42767 .
Since 42767 divided by -42767 is a whole number, -42767 is a factor of 42767
Since 42767 divided by -1 is a whole number, -1 is a factor of 42767
Since 42767 divided by 1 is a whole number, 1 is a factor of 42767
Multiples of 42767 are all integers divisible by 42767 , i.e. the remainder of the full division by 42767 is zero. There are infinite multiples of 42767. The smallest multiples of 42767 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 42767 since 0 × 42767 = 0
42767 : in fact, 42767 is a multiple of itself, since 42767 is divisible by 42767 (it was 42767 / 42767 = 1, so the rest of this division is zero)
85534: in fact, 85534 = 42767 × 2
128301: in fact, 128301 = 42767 × 3
171068: in fact, 171068 = 42767 × 4
213835: in fact, 213835 = 42767 × 5
etc.
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 42767, the answer is: yes, 42767 is a prime number because it only has two different divisors: 1 and itself (42767).
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 42767). 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 206.802 ). 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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