Is 731 a prime number?

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

For 731, the answer is: No, 731 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 731) is as follows: 1, 17, 43, 731.

For 731 to be a prime number, it would have been required that 731 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

731 is a multiple of 1
731 is a multiple of 17
731 is a multiple of 43

For 731 to be a prime number, it would have been required that 731 has only two divisors, i.e., itself and 1.

However, 731 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 731 = 17 x 43, where 17 and 43 are both prime numbers.

Is 731 a deficient number?

Yes, 731 is a deficient number, that is to say 731 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 731 without 731 itself (that is 1 + 17 + 43 = 61).

Parity of 731

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

Find out more:

What is an even number?

Is 731 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 731 is about 27.037.

Thus, the square root of 731 is not an integer, and therefore 731 is not a square number.

What is the square number of 731?

The square of a number (here 731) is the result of the product of this number (731) by itself (i.e., 731 × 731); the square of 731 is sometimes called "raising 731 to the power 2", or "731 squared".

The square of 731 is 534 361 because 731 × 731 = 731² = 534 361.

As a consequence, 731 is the square root of 534 361.

Number of digits of 731

731 is a number with 3 digits.

What are the multiples of 731?

The multiples of 731 are all integers evenly divisible by 731, that is all numbers such that the remainder of the division by 731 is zero. There are infinitely many multiples of 731. The smallest multiples of 731 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 731 too, since 0 × 731 = 0
731: indeed, 731 is a multiple of itself, since 731 is evenly divisible by 731 (we have 731 / 731 = 1, so the remainder of this division is indeed zero)
1 462: indeed, 1 462 = 731 × 2
2 193: indeed, 2 193 = 731 × 3
2 924: indeed, 2 924 = 731 × 4
3 655: indeed, 3 655 = 731 × 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 731). 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 27.037). 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 731

Preceding numbers: …729, 730
Following numbers: 732, 733…

Nearest numbers from 731

Preceding prime number: 727
Following prime number: 733