Is 724 a prime number?

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

For 724, the answer is: No, 724 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 724) is as follows: 1, 2, 4, 181, 362, 724.

For 724 to be a prime number, it would have been required that 724 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

724 is a multiple of 1
724 is a multiple of 2
724 is a multiple of 4
724 is a multiple of 181
724 is a multiple of 362

For 724 to be a prime number, it would have been required that 724 has only two divisors, i.e., itself and 1.

Is 724 a deficient number?

Yes, 724 is a deficient number, that is to say 724 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 724 without 724 itself (that is 1 + 2 + 4 + 181 + 362 = 550).

Parity of 724

724 is an even number, because it is evenly divisible by 2: 724 / 2 = 362.

Find out more:

What is an even number?

Is 724 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 724 is about 26.907.

Thus, the square root of 724 is not an integer, and therefore 724 is not a square number.

What is the square number of 724?

The square of a number (here 724) is the result of the product of this number (724) by itself (i.e., 724 × 724); the square of 724 is sometimes called "raising 724 to the power 2", or "724 squared".

The square of 724 is 524 176 because 724 × 724 = 724² = 524 176.

As a consequence, 724 is the square root of 524 176.

Number of digits of 724

724 is a number with 3 digits.

What are the multiples of 724?

The multiples of 724 are all integers evenly divisible by 724, that is all numbers such that the remainder of the division by 724 is zero. There are infinitely many multiples of 724. The smallest multiples of 724 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 724 too, since 0 × 724 = 0
724: indeed, 724 is a multiple of itself, since 724 is evenly divisible by 724 (we have 724 / 724 = 1, so the remainder of this division is indeed zero)
1 448: indeed, 1 448 = 724 × 2
2 172: indeed, 2 172 = 724 × 3
2 896: indeed, 2 896 = 724 × 4
3 620: indeed, 3 620 = 724 × 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 724). 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 26.907). 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 724

Preceding numbers: …722, 723
Following numbers: 725, 726…

Nearest numbers from 724

Preceding prime number: 719
Following prime number: 727