Is 730 a prime number?

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

For 730, the answer is: No, 730 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 730) is as follows: 1, 2, 5, 10, 73, 146, 365, 730.

For 730 to be a prime number, it would have been required that 730 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 730 cannot be prime, because 5 is one of its divisors: indeed, a number ending with 0 or 5 has necessarily 5 among its divisors. The last digit of 730 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

730 is a multiple of 1
730 is a multiple of 2
730 is a multiple of 5
730 is a multiple of 10
730 is a multiple of 73
730 is a multiple of 146
730 is a multiple of 365

For 730 to be a prime number, it would have been required that 730 has only two divisors, i.e., itself and 1.

Is 730 a deficient number?

Yes, 730 is a deficient number, that is to say 730 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 730 without 730 itself (that is 1 + 2 + 5 + 10 + 73 + 146 + 365 = 602).

Parity of 730

730 is an even number, because it is evenly divisible by 2: 730 / 2 = 365.

Find out more:

What is an even number?

Is 730 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 730 is about 27.019.

Thus, the square root of 730 is not an integer, and therefore 730 is not a square number.

What is the square number of 730?

The square of a number (here 730) is the result of the product of this number (730) by itself (i.e., 730 × 730); the square of 730 is sometimes called "raising 730 to the power 2", or "730 squared".

The square of 730 is 532 900 because 730 × 730 = 730² = 532 900.

As a consequence, 730 is the square root of 532 900.

Number of digits of 730

730 is a number with 3 digits.

What are the multiples of 730?

The multiples of 730 are all integers evenly divisible by 730, that is all numbers such that the remainder of the division by 730 is zero. There are infinitely many multiples of 730. The smallest multiples of 730 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 730 too, since 0 × 730 = 0
730: indeed, 730 is a multiple of itself, since 730 is evenly divisible by 730 (we have 730 / 730 = 1, so the remainder of this division is indeed zero)
1 460: indeed, 1 460 = 730 × 2
2 190: indeed, 2 190 = 730 × 3
2 920: indeed, 2 920 = 730 × 4
3 650: indeed, 3 650 = 730 × 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 730). 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 27.019). 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 730

Preceding numbers: …728, 729
Following numbers: 731, 732…

Nearest numbers from 730

Preceding prime number: 727
Following prime number: 733