It is possible to find out using mathematical methods whether a given integer is a prime number or not.
For 701, the answer is: yes, 701 is a prime number because it has only two distinct divisors: 1 and itself (701).
As a consequence, 701 is only a multiple of 1 and 701..
Since 701 is a prime number, 701 is also a deficient number, that is to say 701 is a natural integer that is strictly larger than the sum of its proper divisors, i.e., the divisors of 701 without 701 itself (that is 1, by definition!).
Parity of 701
701 is an odd number, because it is not evenly divisible by 2.
Is 701 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 701 is about 26.476.
Thus, the square root of 701 is not an integer, and therefore 701 is not a square number.
Anyway, 701 is a prime number, and a prime number cannot be a perfect square.
What is the square number of 701?
The square of a number (here 701) is the result of the product of this number (701) by itself (i.e., 701 × 701); the square of 701 is sometimes called "raising 701 to the power 2", or "701 squared".
As a consequence, 701 is the square root of 491 401.
Number of digits of 701
701 is a number with 3 digits.
What are the multiples of 701?
The multiples of 701 are all integers evenly divisible by 701, that is all numbers such that the remainder of the division by 701 is zero. There are infinitely many multiples of 701. The smallest multiples of 701 are:
- 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 701 too, since 0 × 701 = 0
- 701: indeed, 701 is a multiple of itself, since 701 is evenly divisible by 701 (we have 701 / 701 = 1, so the remainder of this division is indeed zero)
- 1 402: indeed, 1 402 = 701 × 2
- 2 103: indeed, 2 103 = 701 × 3
- 2 804: indeed, 2 804 = 701 × 4
- 3 505: indeed, 3 505 = 701 × 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 701). 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 26.476). 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.