Is 696 a prime number?

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

For 696, the answer is: No, 696 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 696) is as follows: 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696.

For 696 to be a prime number, it would have been required that 696 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

696 is a multiple of 1
696 is a multiple of 2
696 is a multiple of 3
696 is a multiple of 4
696 is a multiple of 6
696 is a multiple of 8
696 is a multiple of 12
696 is a multiple of 24
696 is a multiple of 29
696 is a multiple of 58
696 is a multiple of 87
696 is a multiple of 116
696 is a multiple of 174
696 is a multiple of 232
696 is a multiple of 348

For 696 to be a prime number, it would have been required that 696 has only two divisors, i.e., itself and 1.

Is 696 a deficient number?

No, 696 is not a deficient number: to be deficient, 696 should have been such that 696 is larger than the sum of its proper divisors, i.e., the divisors of 696 without 696 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 29 + 58 + 87 + 116 + 174 + 232 + 348 = 1 104).

In fact, 696 is an abundant number; 696 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 + 29 + 58 + 87 + 116 + 174 + 232 + 348 = 1 104). The smallest abundant number is 12.

Parity of 696

696 is an even number, because it is evenly divisible by 2: 696 / 2 = 348.

Find out more:

What is an even number?

Is 696 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 696 is about 26.382.

Thus, the square root of 696 is not an integer, and therefore 696 is not a square number.

What is the square number of 696?

The square of a number (here 696) is the result of the product of this number (696) by itself (i.e., 696 × 696); the square of 696 is sometimes called "raising 696 to the power 2", or "696 squared".

The square of 696 is 484 416 because 696 × 696 = 696² = 484 416.

As a consequence, 696 is the square root of 484 416.

Number of digits of 696

696 is a number with 3 digits.

What are the multiples of 696?

The multiples of 696 are all integers evenly divisible by 696, that is all numbers such that the remainder of the division by 696 is zero. There are infinitely many multiples of 696. The smallest multiples of 696 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 696 too, since 0 × 696 = 0
696: indeed, 696 is a multiple of itself, since 696 is evenly divisible by 696 (we have 696 / 696 = 1, so the remainder of this division is indeed zero)
1 392: indeed, 1 392 = 696 × 2
2 088: indeed, 2 088 = 696 × 3
2 784: indeed, 2 784 = 696 × 4
3 480: indeed, 3 480 = 696 × 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 696). 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 26.382). 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 696

Preceding numbers: …694, 695
Following numbers: 697, 698…

Nearest numbers from 696

Preceding prime number: 691
Following prime number: 701