Is 25 a prime number?

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

For 25, the answer is: No, 25 is not a prime number.

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

For 25 to be a prime number, it would have been required that 25 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 25 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 25 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

25 is a multiple of 1
25 is a multiple of 5

For 25 to be a prime number, it would have been required that 25 has only two divisors, i.e., itself and 1.

However, 25 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 25 = 5 x 5, where 5 is a prime number.

Is 25 a deficient number?

Yes, 25 is a deficient number, that is to say 25 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 25 without 25 itself (that is 1 + 5 = 6).

Parity of 25

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

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What is an even number?

Is 25 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 25 is 5.

Therefore, the square root of 25 is an integer, and as a consequence 25 is a perfect square.

As a consequence, 5 is the square root of 25.

What is the square number of 25?

The square of a number (here 25) is the result of the product of this number (25) by itself (i.e., 25 × 25); the square of 25 is sometimes called "raising 25 to the power 2", or "25 squared".

The square of 25 is 625 because 25 × 25 = 25² = 625.

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

Number of digits of 25

25 is a number with 2 digits.

What are the multiples of 25?

The multiples of 25 are all integers evenly divisible by 25, that is all numbers such that the remainder of the division by 25 is zero. There are infinitely many multiples of 25. The smallest multiples of 25 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 25 too, since 0 × 25 = 0
25: indeed, 25 is a multiple of itself, since 25 is evenly divisible by 25 (we have 25 / 25 = 1, so the remainder of this division is indeed zero)
50: indeed, 50 = 25 × 2
75: indeed, 75 = 25 × 3
100: indeed, 100 = 25 × 4
125: indeed, 125 = 25 × 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 25). 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 5). 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 25

Preceding numbers: …23, 24
Following numbers: 26, 27…

Nearest numbers from 25

Preceding prime number: 23
Following prime number: 29