Is 125 a prime number?

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

For 125, the answer is: No, 125 is not a prime number.

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

For 125 to be a prime number, it would have been required that 125 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 125 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 125 is 5, so it is divisible by 5 and is therefore not prime.

As a consequence:

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

For 125 to be a prime number, it would have been required that 125 has only two divisors, i.e., itself and 1.

Is 125 a deficient number?

Yes, 125 is a deficient number, that is to say 125 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 125 without 125 itself (that is 1 + 5 + 25 = 31).

Parity of 125

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

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What is an even number?

Is 125 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 125 is about 11.180.

Thus, the square root of 125 is not an integer, and therefore 125 is not a square number.

What is the square number of 125?

The square of a number (here 125) is the result of the product of this number (125) by itself (i.e., 125 × 125); the square of 125 is sometimes called "raising 125 to the power 2", or "125 squared".

The square of 125 is 15 625 because 125 × 125 = 125² = 15 625.

As a consequence, 125 is the square root of 15 625.

Number of digits of 125

125 is a number with 3 digits.

What are the multiples of 125?

The multiples of 125 are all integers evenly divisible by 125, that is all numbers such that the remainder of the division by 125 is zero. There are infinitely many multiples of 125. The smallest multiples of 125 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 125 too, since 0 × 125 = 0
125: indeed, 125 is a multiple of itself, since 125 is evenly divisible by 125 (we have 125 / 125 = 1, so the remainder of this division is indeed zero)
250: indeed, 250 = 125 × 2
375: indeed, 375 = 125 × 3
500: indeed, 500 = 125 × 4
625: indeed, 625 = 125 × 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 125). 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 11.180). 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 125

Preceding numbers: …123, 124
Following numbers: 126, 127…

Nearest numbers from 125

Preceding prime number: 113
Following prime number: 127