Is 711 a prime number?

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

For 711, the answer is: No, 711 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 711) is as follows: 1, 3, 9, 79, 237, 711.

For 711 to be a prime number, it would have been required that 711 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

711 is a multiple of 1
711 is a multiple of 3
711 is a multiple of 9
711 is a multiple of 79
711 is a multiple of 237

For 711 to be a prime number, it would have been required that 711 has only two divisors, i.e., itself and 1.

Is 711 a deficient number?

Yes, 711 is a deficient number, that is to say 711 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 711 without 711 itself (that is 1 + 3 + 9 + 79 + 237 = 329).

Parity of 711

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

Find out more:

What is an even number?

Is 711 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 711 is about 26.665.

Thus, the square root of 711 is not an integer, and therefore 711 is not a square number.

What is the square number of 711?

The square of a number (here 711) is the result of the product of this number (711) by itself (i.e., 711 × 711); the square of 711 is sometimes called "raising 711 to the power 2", or "711 squared".

The square of 711 is 505 521 because 711 × 711 = 711² = 505 521.

As a consequence, 711 is the square root of 505 521.

Number of digits of 711

711 is a number with 3 digits.

What are the multiples of 711?

The multiples of 711 are all integers evenly divisible by 711, that is all numbers such that the remainder of the division by 711 is zero. There are infinitely many multiples of 711. The smallest multiples of 711 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 711 too, since 0 × 711 = 0
711: indeed, 711 is a multiple of itself, since 711 is evenly divisible by 711 (we have 711 / 711 = 1, so the remainder of this division is indeed zero)
1 422: indeed, 1 422 = 711 × 2
2 133: indeed, 2 133 = 711 × 3
2 844: indeed, 2 844 = 711 × 4
3 555: indeed, 3 555 = 711 × 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 711). 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 26.665). 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 711

Preceding numbers: …709, 710
Following numbers: 712, 713…

Nearest numbers from 711

Preceding prime number: 709
Following prime number: 719