Is 721 a prime number?

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

For 721, the answer is: No, 721 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 721) is as follows: 1, 7, 103, 721.

For 721 to be a prime number, it would have been required that 721 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

721 is a multiple of 1
721 is a multiple of 7
721 is a multiple of 103

For 721 to be a prime number, it would have been required that 721 has only two divisors, i.e., itself and 1.

However, 721 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 721 = 7 x 103, where 7 and 103 are both prime numbers.

Is 721 a deficient number?

Yes, 721 is a deficient number, that is to say 721 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 721 without 721 itself (that is 1 + 7 + 103 = 111).

Parity of 721

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

Find out more:

What is an even number?

Is 721 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 721 is about 26.851.

Thus, the square root of 721 is not an integer, and therefore 721 is not a square number.

What is the square number of 721?

The square of a number (here 721) is the result of the product of this number (721) by itself (i.e., 721 × 721); the square of 721 is sometimes called "raising 721 to the power 2", or "721 squared".

The square of 721 is 519 841 because 721 × 721 = 721² = 519 841.

As a consequence, 721 is the square root of 519 841.

Number of digits of 721

721 is a number with 3 digits.

What are the multiples of 721?

The multiples of 721 are all integers evenly divisible by 721, that is all numbers such that the remainder of the division by 721 is zero. There are infinitely many multiples of 721. The smallest multiples of 721 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 721 too, since 0 × 721 = 0
721: indeed, 721 is a multiple of itself, since 721 is evenly divisible by 721 (we have 721 / 721 = 1, so the remainder of this division is indeed zero)
1 442: indeed, 1 442 = 721 × 2
2 163: indeed, 2 163 = 721 × 3
2 884: indeed, 2 884 = 721 × 4
3 605: indeed, 3 605 = 721 × 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 721). 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 26.851). 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 721

Preceding numbers: …719, 720
Following numbers: 722, 723…

Nearest numbers from 721

Preceding prime number: 719
Following prime number: 727