It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 601, the answer is: yes, 601 is a prime number because it has only two distinct divisors: 1 and itself (601).
As a consequence, 601 is only a multiple of 1 and 601..
Since 601 is a prime number, 601 is also a deficient number, that is to say 601 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 601 without 601 itself (that is 1, by definition!).
Parity of 601
601 is an odd number, because it is not evenly divisible by 2.
Is 601 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 601 is about 24.515.
Thus, the square root of 601 is not an integer, and therefore 601 is not a square number.
Anyway, 601 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 601?
The square of a number (here 601) is the result of the product of this number (601) by itself (i.e., 601 × 601); the square of 601 is sometimes called "raising 601 to the power 2", or "601 squared".
As a consequence, 601 is the square root of 361 201.
Number of digits of 601
601 is a number with 3 digits.
What are the multiples of 601?
The multiples of 601 are all integers evenly divisible by 601, that is all numbers such that the remainder of the division by 601 is zero. There are infinitely many multiples of 601. The smallest multiples of 601 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 601 too, since 0 × 601 = 0
- 601: indeed, 601 is a multiple of itself, since 601 is evenly divisible by 601 (we have 601 / 601 = 1, so the remainder of this division is indeed zero)
- 1 202: indeed, 1 202 = 601 × 2
- 1 803: indeed, 1 803 = 601 × 3
- 2 404: indeed, 2 404 = 601 × 4
- 3 005: indeed, 3 005 = 601 × 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 601). 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 24.515). 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.