Is 249 a prime number?

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

For 249, the answer is: No, 249 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 249) is as follows: 1, 3, 83, 249.

For 249 to be a prime number, it would have been required that 249 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

249 is a multiple of 1
249 is a multiple of 3
249 is a multiple of 83

For 249 to be a prime number, it would have been required that 249 has only two divisors, i.e., itself and 1.

However, 249 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 249 = 3 x 83, where 3 and 83 are both prime numbers.

Is 249 a deficient number?

Yes, 249 is a deficient number, that is to say 249 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 249 without 249 itself (that is 1 + 3 + 83 = 87).

Parity of 249

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

Find out more:

What is an even number?

Is 249 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 249 is about 15.780.

Thus, the square root of 249 is not an integer, and therefore 249 is not a square number.

What is the square number of 249?

The square of a number (here 249) is the result of the product of this number (249) by itself (i.e., 249 × 249); the square of 249 is sometimes called "raising 249 to the power 2", or "249 squared".

The square of 249 is 62 001 because 249 × 249 = 249² = 62 001.

As a consequence, 249 is the square root of 62 001.

Number of digits of 249

249 is a number with 3 digits.

What are the multiples of 249?

The multiples of 249 are all integers evenly divisible by 249, that is all numbers such that the remainder of the division by 249 is zero. There are infinitely many multiples of 249. The smallest multiples of 249 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 249 too, since 0 × 249 = 0
249: indeed, 249 is a multiple of itself, since 249 is evenly divisible by 249 (we have 249 / 249 = 1, so the remainder of this division is indeed zero)
498: indeed, 498 = 249 × 2
747: indeed, 747 = 249 × 3
996: indeed, 996 = 249 × 4
1 245: indeed, 1 245 = 249 × 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 249). 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 15.780). 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 249

Preceding numbers: …247, 248
Following numbers: 250, 251…

Nearest numbers from 249

Preceding prime number: 241
Following prime number: 251