It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 479, the answer is: yes, 479 is a prime number because it has only two distinct divisors: 1 and itself (479).
As a consequence, 479 is only a multiple of 1 and 479..
Since 479 is a prime number, 479 is also a deficient number, that is to say 479 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 479 without 479 itself (that is 1, by definition!).
Parity of 479
479 is an odd number, because it is not evenly divisible by 2.
Is 479 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 479 is about 21.886.
Thus, the square root of 479 is not an integer, and therefore 479 is not a square number.
Anyway, 479 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 479?
The square of a number (here 479) is the result of the product of this number (479) by itself (i.e., 479 × 479); the square of 479 is sometimes called "raising 479 to the power 2", or "479 squared".
As a consequence, 479 is the square root of 229 441.
Number of digits of 479
479 is a number with 3 digits.
What are the multiples of 479?
The multiples of 479 are all integers evenly divisible by 479, that is all numbers such that the remainder of the division by 479 is zero. There are infinitely many multiples of 479. The smallest multiples of 479 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 479 too, since 0 × 479 = 0
- 479: indeed, 479 is a multiple of itself, since 479 is evenly divisible by 479 (we have 479 / 479 = 1, so the remainder of this division is indeed zero)
- 958: indeed, 958 = 479 × 2
- 1 437: indeed, 1 437 = 479 × 3
- 1 916: indeed, 1 916 = 479 × 4
- 2 395: indeed, 2 395 = 479 × 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 479). 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 21.886). 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.