It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 967, the answer is: yes, 967 is a prime number because it has only two distinct divisors: 1 and itself (967).
As a consequence, 967 is only a multiple of 1 and 967..
Since 967 is a prime number, 967 is also a deficient number, that is to say 967 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 967 without 967 itself (that is 1, by definition!).
Parity of 967
967 is an odd number, because it is not evenly divisible by 2.
Is 967 a perfect square number?
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 967 is about 31.097.
Thus, the square root of 967 is not an integer, and therefore 967 is not a square number.
Anyway, 967 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 967?
The square of a number (here 967) is the result of the product of this number (967) by itself (i.e., 967 × 967); the square of 967 is sometimes called "raising 967 to the power 2", or "967 squared".
As a consequence, 967 is the square root of 935 089.
Number of digits of 967
967 is a number with 3 digits.
What are the multiples of 967?
The multiples of 967 are all integers evenly divisible by 967, that is all numbers such that the remainder of the division by 967 is zero. There are infinitely many multiples of 967. The smallest multiples of 967 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 967 too, since 0 × 967 = 0
- 967: indeed, 967 is a multiple of itself, since 967 is evenly divisible by 967 (we have 967 / 967 = 1, so the remainder of this division is indeed zero)
- 1 934: indeed, 1 934 = 967 × 2
- 2 901: indeed, 2 901 = 967 × 3
- 3 868: indeed, 3 868 = 967 × 4
- 4 835: indeed, 4 835 = 967 × 5
How to determine whether an integer is a prime number?
To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality (here 967). First, we can eliminate all even numbers greater than 2 (and hence 4, 6, 8…). Then, we can stop this check when we reach the square root of the number of which we want to determine the primality (here the square root is about 31.097). Historically, the sieve of Eratosthenes (dating from the Greek mathematics) implements this technique in a relatively efficient manner.
More modern techniques include the sieve of Atkin, probabilistic algorithms, and the cyclotomic AKS test.