It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 929, the answer is: yes, 929 is a prime number because it has only two distinct divisors: 1 and itself (929).
As a consequence, 929 is only a multiple of 1 and 929..
Since 929 is a prime number, 929 is also a deficient number, that is to say 929 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 929 without 929 itself (that is 1, by definition!).
Parity of 929
929 is an odd number, because it is not evenly divisible by 2.
Is 929 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 929 is about 30.480.
Thus, the square root of 929 is not an integer, and therefore 929 is not a square number.
Anyway, 929 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 929?
The square of a number (here 929) is the result of the product of this number (929) by itself (i.e., 929 × 929); the square of 929 is sometimes called "raising 929 to the power 2", or "929 squared".
As a consequence, 929 is the square root of 863 041.
Number of digits of 929
929 is a number with 3 digits.
What are the multiples of 929?
The multiples of 929 are all integers evenly divisible by 929, that is all numbers such that the remainder of the division by 929 is zero. There are infinitely many multiples of 929. The smallest multiples of 929 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 929 too, since 0 × 929 = 0
- 929: indeed, 929 is a multiple of itself, since 929 is evenly divisible by 929 (we have 929 / 929 = 1, so the remainder of this division is indeed zero)
- 1 858: indeed, 1 858 = 929 × 2
- 2 787: indeed, 2 787 = 929 × 3
- 3 716: indeed, 3 716 = 929 × 4
- 4 645: indeed, 4 645 = 929 × 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 929). 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 30.480). 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.