Is 722 a prime number?

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

For 722, the answer is: No, 722 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 722) is as follows: 1, 2, 19, 38, 361, 722.

For 722 to be a prime number, it would have been required that 722 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

722 is a multiple of 1
722 is a multiple of 2
722 is a multiple of 19
722 is a multiple of 38
722 is a multiple of 361

For 722 to be a prime number, it would have been required that 722 has only two divisors, i.e., itself and 1.

Is 722 a deficient number?

Yes, 722 is a deficient number, that is to say 722 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 722 without 722 itself (that is 1 + 2 + 19 + 38 + 361 = 421).

Parity of 722

722 is an even number, because it is evenly divisible by 2: 722 / 2 = 361.

Find out more:

What is an even number?

Is 722 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 722 is about 26.870.

Thus, the square root of 722 is not an integer, and therefore 722 is not a square number.

What is the square number of 722?

The square of a number (here 722) is the result of the product of this number (722) by itself (i.e., 722 × 722); the square of 722 is sometimes called "raising 722 to the power 2", or "722 squared".

The square of 722 is 521 284 because 722 × 722 = 722² = 521 284.

As a consequence, 722 is the square root of 521 284.

Number of digits of 722

722 is a number with 3 digits.

What are the multiples of 722?

The multiples of 722 are all integers evenly divisible by 722, that is all numbers such that the remainder of the division by 722 is zero. There are infinitely many multiples of 722. The smallest multiples of 722 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 722 too, since 0 × 722 = 0
722: indeed, 722 is a multiple of itself, since 722 is evenly divisible by 722 (we have 722 / 722 = 1, so the remainder of this division is indeed zero)
1 444: indeed, 1 444 = 722 × 2
2 166: indeed, 2 166 = 722 × 3
2 888: indeed, 2 888 = 722 × 4
3 610: indeed, 3 610 = 722 × 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 722). 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 26.870). 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 722

Preceding numbers: …720, 721
Following numbers: 723, 724…

Nearest numbers from 722

Preceding prime number: 719
Following prime number: 727