Is 697 a prime number?

It is possible to find out using mathematical methods whether a given integer is a prime number or not.

For 697, the answer is: No, 697 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 697) is as follows: 1, 17, 41, 697.

For 697 to be a prime number, it would have been required that 697 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

697 is a multiple of 1
697 is a multiple of 17
697 is a multiple of 41

For 697 to be a prime number, it would have been required that 697 has only two divisors, i.e., itself and 1.

However, 697 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 697 = 17 x 41, where 17 and 41 are both prime numbers.

Is 697 a deficient number?

Yes, 697 is a deficient number, that is to say 697 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 697 without 697 itself (that is 1 + 17 + 41 = 59).

Parity of 697

697 is an odd number, because it is not evenly divisible by 2.

Find out more:

What is an even number?

Is 697 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 697 is about 26.401.

Thus, the square root of 697 is not an integer, and therefore 697 is not a square number.

What is the square number of 697?

The square of a number (here 697) is the result of the product of this number (697) by itself (i.e., 697 × 697); the square of 697 is sometimes called "raising 697 to the power 2", or "697 squared".

The square of 697 is 485 809 because 697 × 697 = 697² = 485 809.

As a consequence, 697 is the square root of 485 809.

Number of digits of 697

697 is a number with 3 digits.

What are the multiples of 697?

The multiples of 697 are all integers evenly divisible by 697, that is all numbers such that the remainder of the division by 697 is zero. There are infinitely many multiples of 697. The smallest multiples of 697 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 697 too, since 0 × 697 = 0
697: indeed, 697 is a multiple of itself, since 697 is evenly divisible by 697 (we have 697 / 697 = 1, so the remainder of this division is indeed zero)
1 394: indeed, 1 394 = 697 × 2
2 091: indeed, 2 091 = 697 × 3
2 788: indeed, 2 788 = 697 × 4
3 485: indeed, 3 485 = 697 × 5
etc.

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 697). 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 26.401). 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.

Numbers near 697

Preceding numbers: …695, 696
Following numbers: 698, 699…

Nearest numbers from 697

Preceding prime number: 691
Following prime number: 701