Is 712 a prime number? What are the divisors of 712?

Is 712 a prime number?

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

For 712, the answer is: No, 712 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 712) is as follows: 1, 2, 4, 8, 89, 178, 356, 712.

To be 712 a prime number, it would have been required that 712 has only two divisors, i.e., itself and 1.

As a consequence:

  • 712 is a multiple of 1
  • 712 is a multiple of 2
  • 712 is a multiple of 4
  • 712 is a multiple of 8
  • 712 is a multiple of 89
  • 712 is a multiple of 178
  • 712 is a multiple of 356

To be 712 a prime number, it would have been required that 712 has only two divisors, i.e., itself and 1.

Is 712 a deficient number?

Yes, 712 is a deficient number, that is to say 712 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 712 without 712 itself (that is 1 + 2 + 4 + 8 + 89 + 178 + 356 = 638).

Parity of 712

712 is an even number, because it is evenly divisible by 2: 712 / 2 = 356.

Is 712 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 712 is about 26.683.

Thus, the square root of 712 is not an integer, and therefore 712 is not a square number.

What is the square number of 712?

The square of a number (here 712) is the result of the product of this number (712) by itself (i.e., 712 × 712); the square of 712 is sometimes called "raising 712 to the power 2", or "712 squared".

The square of 712 is 506 944 because 712 × 712 = 7122 = 506 944.

As a consequence, 712 is the square root of 506 944.

Number of digits of 712

712 is a number with 3 digits.

What are the multiples of 712?

The multiples of 712 are all integers evenly divisible by 712, that is all numbers such that the remainder of the division by 712 is zero. There are infinitely many multiples of 712. The smallest multiples of 712 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 712 too, since 0 × 712 = 0
  • 712: indeed, 712 is a multiple of itself, since 712 is evenly divisible by 712 (we have 712 / 712 = 1, so the remainder of this division is indeed zero)
  • 1 424: indeed, 1 424 = 712 × 2
  • 2 136: indeed, 2 136 = 712 × 3
  • 2 848: indeed, 2 848 = 712 × 4
  • 3 560: indeed, 3 560 = 712 × 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 712). 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 26.683). 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 712

  • Preceding numbers: …710, 711
  • Following numbers: 713, 714

Nearest numbers from 712

  • Preceding prime number: 709
  • Following prime number: 719
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