It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 661, the answer is: yes, 661 is a prime number because it has only two distinct divisors: 1 and itself (661).
As a consequence, 661 is only a multiple of 1 and 661..
Since 661 is a prime number, 661 is also a deficient number, that is to say 661 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 661 without 661 itself (that is 1, by definition!).
Parity of 661
661 is an odd number, because it is not evenly divisible by 2.
Is 661 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 661 is about 25.710.
Thus, the square root of 661 is not an integer, and therefore 661 is not a square number.
Anyway, 661 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 661?
The square of a number (here 661) is the result of the product of this number (661) by itself (i.e., 661 × 661); the square of 661 is sometimes called "raising 661 to the power 2", or "661 squared".
As a consequence, 661 is the square root of 436 921.
Number of digits of 661
661 is a number with 3 digits.
What are the multiples of 661?
The multiples of 661 are all integers evenly divisible by 661, that is all numbers such that the remainder of the division by 661 is zero. There are infinitely many multiples of 661. The smallest multiples of 661 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 661 too, since 0 × 661 = 0
- 661: indeed, 661 is a multiple of itself, since 661 is evenly divisible by 661 (we have 661 / 661 = 1, so the remainder of this division is indeed zero)
- 1 322: indeed, 1 322 = 661 × 2
- 1 983: indeed, 1 983 = 661 × 3
- 2 644: indeed, 2 644 = 661 × 4
- 3 305: indeed, 3 305 = 661 × 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 661). 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 25.710). 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.