967is an odd number,as it is not divisible by 2
The factors for 967 are all the numbers between -967 and 967 , which divide 967 without leaving any remainder. Since 967 divided by -967 is an integer, -967 is a factor of 967 .
Since 967 divided by -967 is a whole number, -967 is a factor of 967
Since 967 divided by -1 is a whole number, -1 is a factor of 967
Since 967 divided by 1 is a whole number, 1 is a factor of 967
Multiples of 967 are all integers divisible by 967 , i.e. the remainder of the full division by 967 is zero. There are infinite multiples of 967. The smallest multiples of 967 are:
0 : in fact, 0 is divisible by any integer, so it is also a multiple of 967 since 0 × 967 = 0
967 : in fact, 967 is a multiple of itself, since 967 is divisible by 967 (it was 967 / 967 = 1, so the rest of this division is zero)
It is possible to determine using mathematical techniques whether an integer is prime or not.
for 967, the answer is: yes, 967 is a prime number because it only has two different divisors: 1 and itself (967).
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 967). 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 31.097 ). 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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