Is 723 a prime number?

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

For 723, the answer is: No, 723 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 723) is as follows: 1, 3, 241, 723.

For 723 to be a prime number, it would have been required that 723 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

723 is a multiple of 1
723 is a multiple of 3
723 is a multiple of 241

For 723 to be a prime number, it would have been required that 723 has only two divisors, i.e., itself and 1.

However, 723 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 723 = 3 x 241, where 3 and 241 are both prime numbers.

Is 723 a deficient number?

Yes, 723 is a deficient number, that is to say 723 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 723 without 723 itself (that is 1 + 3 + 241 = 245).

Parity of 723

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

Find out more:

What is an even number?

Is 723 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 723 is about 26.889.

Thus, the square root of 723 is not an integer, and therefore 723 is not a square number.

What is the square number of 723?

The square of a number (here 723) is the result of the product of this number (723) by itself (i.e., 723 × 723); the square of 723 is sometimes called "raising 723 to the power 2", or "723 squared".

The square of 723 is 522 729 because 723 × 723 = 723² = 522 729.

As a consequence, 723 is the square root of 522 729.

Number of digits of 723

723 is a number with 3 digits.

What are the multiples of 723?

The multiples of 723 are all integers evenly divisible by 723, that is all numbers such that the remainder of the division by 723 is zero. There are infinitely many multiples of 723. The smallest multiples of 723 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 723 too, since 0 × 723 = 0
723: indeed, 723 is a multiple of itself, since 723 is evenly divisible by 723 (we have 723 / 723 = 1, so the remainder of this division is indeed zero)
1 446: indeed, 1 446 = 723 × 2
2 169: indeed, 2 169 = 723 × 3
2 892: indeed, 2 892 = 723 × 4
3 615: indeed, 3 615 = 723 × 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 723). 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 26.889). 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 723

Preceding numbers: …721, 722
Following numbers: 724, 725…

Nearest numbers from 723

Preceding prime number: 719
Following prime number: 727