Is 693 a prime number?

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

For 693, the answer is: No, 693 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 693) is as follows: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693.

For 693 to be a prime number, it would have been required that 693 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

693 is a multiple of 1
693 is a multiple of 3
693 is a multiple of 7
693 is a multiple of 9
693 is a multiple of 11
693 is a multiple of 21
693 is a multiple of 33
693 is a multiple of 63
693 is a multiple of 77
693 is a multiple of 99
693 is a multiple of 231

For 693 to be a prime number, it would have been required that 693 has only two divisors, i.e., itself and 1.

Is 693 a deficient number?

Yes, 693 is a deficient number, that is to say 693 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 693 without 693 itself (that is 1 + 3 + 7 + 9 + 11 + 21 + 33 + 63 + 77 + 99 + 231 = 555).

Parity of 693

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

Find out more:

What is an even number?

Is 693 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 693 is about 26.325.

Thus, the square root of 693 is not an integer, and therefore 693 is not a square number.

What is the square number of 693?

The square of a number (here 693) is the result of the product of this number (693) by itself (i.e., 693 × 693); the square of 693 is sometimes called "raising 693 to the power 2", or "693 squared".

The square of 693 is 480 249 because 693 × 693 = 693² = 480 249.

As a consequence, 693 is the square root of 480 249.

Number of digits of 693

693 is a number with 3 digits.

What are the multiples of 693?

The multiples of 693 are all integers evenly divisible by 693, that is all numbers such that the remainder of the division by 693 is zero. There are infinitely many multiples of 693. The smallest multiples of 693 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 693 too, since 0 × 693 = 0
693: indeed, 693 is a multiple of itself, since 693 is evenly divisible by 693 (we have 693 / 693 = 1, so the remainder of this division is indeed zero)
1 386: indeed, 1 386 = 693 × 2
2 079: indeed, 2 079 = 693 × 3
2 772: indeed, 2 772 = 693 × 4
3 465: indeed, 3 465 = 693 × 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 693). 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 26.325). 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 693

Preceding numbers: …691, 692
Following numbers: 694, 695…

Nearest numbers from 693

Preceding prime number: 691
Following prime number: 701