Is 726 a prime number?

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

For 726, the answer is: No, 726 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 726) is as follows: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.

For 726 to be a prime number, it would have been required that 726 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

726 is a multiple of 1
726 is a multiple of 2
726 is a multiple of 3
726 is a multiple of 6
726 is a multiple of 11
726 is a multiple of 22
726 is a multiple of 33
726 is a multiple of 66
726 is a multiple of 121
726 is a multiple of 242
726 is a multiple of 363

For 726 to be a prime number, it would have been required that 726 has only two divisors, i.e., itself and 1.

Is 726 a deficient number?

No, 726 is not a deficient number: to be deficient, 726 should have been such that 726 is larger than the sum of its proper divisors, i.e., the divisors of 726 without 726 itself (that is 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 + 121 + 242 + 363 = 870).

In fact, 726 is an abundant number; 726 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 + 121 + 242 + 363 = 870). The smallest abundant number is 12.

Parity of 726

726 is an even number, because it is evenly divisible by 2: 726 / 2 = 363.

Find out more:

What is an even number?

Is 726 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 726 is about 26.944.

Thus, the square root of 726 is not an integer, and therefore 726 is not a square number.

What is the square number of 726?

The square of a number (here 726) is the result of the product of this number (726) by itself (i.e., 726 × 726); the square of 726 is sometimes called "raising 726 to the power 2", or "726 squared".

The square of 726 is 527 076 because 726 × 726 = 726² = 527 076.

As a consequence, 726 is the square root of 527 076.

Number of digits of 726

726 is a number with 3 digits.

What are the multiples of 726?

The multiples of 726 are all integers evenly divisible by 726, that is all numbers such that the remainder of the division by 726 is zero. There are infinitely many multiples of 726. The smallest multiples of 726 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 726 too, since 0 × 726 = 0
726: indeed, 726 is a multiple of itself, since 726 is evenly divisible by 726 (we have 726 / 726 = 1, so the remainder of this division is indeed zero)
1 452: indeed, 1 452 = 726 × 2
2 178: indeed, 2 178 = 726 × 3
2 904: indeed, 2 904 = 726 × 4
3 630: indeed, 3 630 = 726 × 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 726). 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 26.944). 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 726

Preceding numbers: …724, 725
Following numbers: 727, 728…

Nearest numbers from 726

Preceding prime number: 719
Following prime number: 727