It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 487, the answer is: yes, 487 is a prime number because it has only two distinct divisors: 1 and itself (487).
As a consequence, 487 is only a multiple of 1 and 487..
Since 487 is a prime number, 487 is also a deficient number, that is to say 487 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 487 without 487 itself (that is 1, by definition!).
Parity of 487
487 is an odd number, because it is not evenly divisible by 2.
Is 487 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 487 is about 22.068.
Thus, the square root of 487 is not an integer, and therefore 487 is not a square number.
Anyway, 487 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 487?
The square of a number (here 487) is the result of the product of this number (487) by itself (i.e., 487 × 487); the square of 487 is sometimes called "raising 487 to the power 2", or "487 squared".
As a consequence, 487 is the square root of 237 169.
Number of digits of 487
487 is a number with 3 digits.
What are the multiples of 487?
The multiples of 487 are all integers evenly divisible by 487, that is all numbers such that the remainder of the division by 487 is zero. There are infinitely many multiples of 487. The smallest multiples of 487 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 487 too, since 0 × 487 = 0
- 487: indeed, 487 is a multiple of itself, since 487 is evenly divisible by 487 (we have 487 / 487 = 1, so the remainder of this division is indeed zero)
- 974: indeed, 974 = 487 × 2
- 1 461: indeed, 1 461 = 487 × 3
- 1 948: indeed, 1 948 = 487 × 4
- 2 435: indeed, 2 435 = 487 × 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 487). 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 22.068). 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.