Is 625 a prime number?

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

For 625, the answer is: No, 625 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 625) is as follows: 1, 5, 25, 125, 625.

For 625 to be a prime number, it would have been required that 625 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 625 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 625 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

625 is a multiple of 1
625 is a multiple of 5
625 is a multiple of 25
625 is a multiple of 125

For 625 to be a prime number, it would have been required that 625 has only two divisors, i.e., itself and 1.

Is 625 a deficient number?

Yes, 625 is a deficient number, that is to say 625 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 625 without 625 itself (that is 1 + 5 + 25 + 125 = 156).

Parity of 625

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

Find out more:

What is an even number?

Is 625 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 625 is 25.

Therefore, the square root of 625 is an integer, and as a consequence 625 is a perfect square.

As a consequence, 25 is the square root of 625.

What is the square number of 625?

The square of a number (here 625) is the result of the product of this number (625) by itself (i.e., 625 × 625); the square of 625 is sometimes called "raising 625 to the power 2", or "625 squared".

The square of 625 is 390 625 because 625 × 625 = 625² = 390 625.

As a consequence, 625 is the square root of 390 625.

Number of digits of 625

625 is a number with 3 digits.

What are the multiples of 625?

The multiples of 625 are all integers evenly divisible by 625, that is all numbers such that the remainder of the division by 625 is zero. There are infinitely many multiples of 625. The smallest multiples of 625 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 625 too, since 0 × 625 = 0
625: indeed, 625 is a multiple of itself, since 625 is evenly divisible by 625 (we have 625 / 625 = 1, so the remainder of this division is indeed zero)
1 250: indeed, 1 250 = 625 × 2
1 875: indeed, 1 875 = 625 × 3
2 500: indeed, 2 500 = 625 × 4
3 125: indeed, 3 125 = 625 × 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 625). 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 25). 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 625

Preceding numbers: …623, 624
Following numbers: 626, 627…

Nearest numbers from 625

Preceding prime number: 619
Following prime number: 631