Is 728 a prime number?

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

For 728, the answer is: No, 728 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 728) is as follows: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.

For 728 to be a prime number, it would have been required that 728 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

728 is a multiple of 1
728 is a multiple of 2
728 is a multiple of 4
728 is a multiple of 7
728 is a multiple of 8
728 is a multiple of 13
728 is a multiple of 14
728 is a multiple of 26
728 is a multiple of 28
728 is a multiple of 52
728 is a multiple of 56
728 is a multiple of 91
728 is a multiple of 104
728 is a multiple of 182
728 is a multiple of 364

For 728 to be a prime number, it would have been required that 728 has only two divisors, i.e., itself and 1.

Is 728 a deficient number?

No, 728 is not a deficient number: to be deficient, 728 should have been such that 728 is larger than the sum of its proper divisors, i.e., the divisors of 728 without 728 itself (that is 1 + 2 + 4 + 7 + 8 + 13 + 14 + 26 + 28 + 52 + 56 + 91 + 104 + 182 + 364 = 952).

In fact, 728 is an abundant number; 728 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 4 + 7 + 8 + 13 + 14 + 26 + 28 + 52 + 56 + 91 + 104 + 182 + 364 = 952). The smallest abundant number is 12.

Parity of 728

728 is an even number, because it is evenly divisible by 2: 728 / 2 = 364.

Find out more:

What is an even number?

Is 728 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 728 is about 26.981.

Thus, the square root of 728 is not an integer, and therefore 728 is not a square number.

What is the square number of 728?

The square of a number (here 728) is the result of the product of this number (728) by itself (i.e., 728 × 728); the square of 728 is sometimes called "raising 728 to the power 2", or "728 squared".

The square of 728 is 529 984 because 728 × 728 = 728² = 529 984.

As a consequence, 728 is the square root of 529 984.

Number of digits of 728

728 is a number with 3 digits.

What are the multiples of 728?

The multiples of 728 are all integers evenly divisible by 728, that is all numbers such that the remainder of the division by 728 is zero. There are infinitely many multiples of 728. The smallest multiples of 728 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 728 too, since 0 × 728 = 0
728: indeed, 728 is a multiple of itself, since 728 is evenly divisible by 728 (we have 728 / 728 = 1, so the remainder of this division is indeed zero)
1 456: indeed, 1 456 = 728 × 2
2 184: indeed, 2 184 = 728 × 3
2 912: indeed, 2 912 = 728 × 4
3 640: indeed, 3 640 = 728 × 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 728). 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 26.981). 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 728

Preceding numbers: …726, 727
Following numbers: 729, 730…

Nearest numbers from 728

Preceding prime number: 727
Following prime number: 733