Is 713 a prime number? What are the divisors of 713?

Is 713 a prime number?

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

For 713, the answer is: No, 713 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 713) is as follows: 1, 23, 31, 713.

To be 713 a prime number, it would have been required that 713 has only two divisors, i.e., itself and 1.

As a consequence:

  • 713 is a multiple of 1
  • 713 is a multiple of 23
  • 713 is a multiple of 31

To be 713 a prime number, it would have been required that 713 has only two divisors, i.e., itself and 1.

However, 713 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 713 = 23 x 31, where 23 and 31 are both prime numbers.

Is 713 a deficient number?

Yes, 713 is a deficient number, that is to say 713 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 713 without 713 itself (that is 1 + 23 + 31 = 55).

Parity of 713

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

Is 713 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 713 is about 26.702.

Thus, the square root of 713 is not an integer, and therefore 713 is not a square number.

What is the square number of 713?

The square of a number (here 713) is the result of the product of this number (713) by itself (i.e., 713 × 713); the square of 713 is sometimes called "raising 713 to the power 2", or "713 squared".

The square of 713 is 508 369 because 713 × 713 = 7132 = 508 369.

As a consequence, 713 is the square root of 508 369.

Number of digits of 713

713 is a number with 3 digits.

What are the multiples of 713?

The multiples of 713 are all integers evenly divisible by 713, that is all numbers such that the remainder of the division by 713 is zero. There are infinitely many multiples of 713. The smallest multiples of 713 are:

  • 0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 713 too, since 0 × 713 = 0
  • 713: indeed, 713 is a multiple of itself, since 713 is evenly divisible by 713 (we have 713 / 713 = 1, so the remainder of this division is indeed zero)
  • 1 426: indeed, 1 426 = 713 × 2
  • 2 139: indeed, 2 139 = 713 × 3
  • 2 852: indeed, 2 852 = 713 × 4
  • 3 565: indeed, 3 565 = 713 × 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 713). 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 26.702). 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 713

  • Preceding numbers: …711, 712
  • Following numbers: 714, 715

Nearest numbers from 713

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