Is 250 a prime number?

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

For 250, the answer is: No, 250 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 250) is as follows: 1, 2, 5, 10, 25, 50, 125, 250.

For 250 to be a prime number, it would have been required that 250 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

Actually, one can immediately see that 250 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 250 is 0, so it is divisible by 5 and is therefore not prime.

As a consequence:

250 is a multiple of 1
250 is a multiple of 2
250 is a multiple of 5
250 is a multiple of 10
250 is a multiple of 25
250 is a multiple of 50
250 is a multiple of 125

For 250 to be a prime number, it would have been required that 250 has only two divisors, i.e., itself and 1.

Is 250 a deficient number?

Yes, 250 is a deficient number, that is to say 250 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 250 without 250 itself (that is 1 + 2 + 5 + 10 + 25 + 50 + 125 = 218).

Parity of 250

250 is an even number, because it is evenly divisible by 2: 250 / 2 = 125.

Find out more:

What is an even number?

Is 250 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 250 is about 15.811.

Thus, the square root of 250 is not an integer, and therefore 250 is not a square number.

What is the square number of 250?

The square of a number (here 250) is the result of the product of this number (250) by itself (i.e., 250 × 250); the square of 250 is sometimes called "raising 250 to the power 2", or "250 squared".

The square of 250 is 62 500 because 250 × 250 = 250² = 62 500.

As a consequence, 250 is the square root of 62 500.

Number of digits of 250

250 is a number with 3 digits.

What are the multiples of 250?

The multiples of 250 are all integers evenly divisible by 250, that is all numbers such that the remainder of the division by 250 is zero. There are infinitely many multiples of 250. The smallest multiples of 250 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 250 too, since 0 × 250 = 0
250: indeed, 250 is a multiple of itself, since 250 is evenly divisible by 250 (we have 250 / 250 = 1, so the remainder of this division is indeed zero)
500: indeed, 500 = 250 × 2
750: indeed, 750 = 250 × 3
1 000: indeed, 1 000 = 250 × 4
1 250: indeed, 1 250 = 250 × 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 250). 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 15.811). 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 250

Preceding numbers: …248, 249
Following numbers: 251, 252…

Nearest numbers from 250

Preceding prime number: 241
Following prime number: 251