Is 729 a prime number?

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

For 729, the answer is: No, 729 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 729) is as follows: 1, 3, 9, 27, 81, 243, 729.

For 729 to be a prime number, it would have been required that 729 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

729 is a multiple of 1
729 is a multiple of 3
729 is a multiple of 9
729 is a multiple of 27
729 is a multiple of 81
729 is a multiple of 243

For 729 to be a prime number, it would have been required that 729 has only two divisors, i.e., itself and 1.

Is 729 a deficient number?

Yes, 729 is a deficient number, that is to say 729 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 729 without 729 itself (that is 1 + 3 + 9 + 27 + 81 + 243 = 364).

Parity of 729

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

Find out more:

What is an even number?

Is 729 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 729 is 27.

Therefore, the square root of 729 is an integer, and as a consequence 729 is a perfect square.

As a consequence, 27 is the square root of 729.

What is the square number of 729?

The square of a number (here 729) is the result of the product of this number (729) by itself (i.e., 729 × 729); the square of 729 is sometimes called "raising 729 to the power 2", or "729 squared".

The square of 729 is 531 441 because 729 × 729 = 729² = 531 441.

As a consequence, 729 is the square root of 531 441.

Number of digits of 729

729 is a number with 3 digits.

What are the multiples of 729?

The multiples of 729 are all integers evenly divisible by 729, that is all numbers such that the remainder of the division by 729 is zero. There are infinitely many multiples of 729. The smallest multiples of 729 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 729 too, since 0 × 729 = 0
729: indeed, 729 is a multiple of itself, since 729 is evenly divisible by 729 (we have 729 / 729 = 1, so the remainder of this division is indeed zero)
1 458: indeed, 1 458 = 729 × 2
2 187: indeed, 2 187 = 729 × 3
2 916: indeed, 2 916 = 729 × 4
3 645: indeed, 3 645 = 729 × 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 729). 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 27). 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 729

Preceding numbers: …727, 728
Following numbers: 730, 731…

Nearest numbers from 729

Preceding prime number: 727
Following prime number: 733