Is 725 a prime number?

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

For 725, the answer is: No, 725 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 725) is as follows: 1, 5, 25, 29, 145, 725.

For 725 to be a prime number, it would have been required that 725 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 725 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 725 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

725 is a multiple of 1
725 is a multiple of 5
725 is a multiple of 25
725 is a multiple of 29
725 is a multiple of 145

For 725 to be a prime number, it would have been required that 725 has only two divisors, i.e., itself and 1.

Is 725 a deficient number?

Yes, 725 is a deficient number, that is to say 725 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 725 without 725 itself (that is 1 + 5 + 25 + 29 + 145 = 205).

Parity of 725

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

Find out more:

What is an even number?

Is 725 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 725 is about 26.926.

Thus, the square root of 725 is not an integer, and therefore 725 is not a square number.

What is the square number of 725?

The square of a number (here 725) is the result of the product of this number (725) by itself (i.e., 725 × 725); the square of 725 is sometimes called "raising 725 to the power 2", or "725 squared".

The square of 725 is 525 625 because 725 × 725 = 725² = 525 625.

As a consequence, 725 is the square root of 525 625.

Number of digits of 725

725 is a number with 3 digits.

What are the multiples of 725?

The multiples of 725 are all integers evenly divisible by 725, that is all numbers such that the remainder of the division by 725 is zero. There are infinitely many multiples of 725. The smallest multiples of 725 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 725 too, since 0 × 725 = 0
725: indeed, 725 is a multiple of itself, since 725 is evenly divisible by 725 (we have 725 / 725 = 1, so the remainder of this division is indeed zero)
1 450: indeed, 1 450 = 725 × 2
2 175: indeed, 2 175 = 725 × 3
2 900: indeed, 2 900 = 725 × 4
3 625: indeed, 3 625 = 725 × 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 725). 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 26.926). 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 725

Preceding numbers: …723, 724
Following numbers: 726, 727…

Nearest numbers from 725

Preceding prime number: 719
Following prime number: 727