Is 253 a prime number?

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

For 253, the answer is: No, 253 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 253) is as follows: 1, 11, 23, 253.

For 253 to be a prime number, it would have been required that 253 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

253 is a multiple of 1
253 is a multiple of 11
253 is a multiple of 23

For 253 to be a prime number, it would have been required that 253 has only two divisors, i.e., itself and 1.

However, 253 is a semiprime (also called biprime or 2-almost-prime), because it is the product of a two non-necessarily distinct prime numbers. Indeed, 253 = 11 x 23, where 11 and 23 are both prime numbers.

Is 253 a deficient number?

Yes, 253 is a deficient number, that is to say 253 is a natural number that is strictly larger than the sum of its proper divisors, i.e., the divisors of 253 without 253 itself (that is 1 + 11 + 23 = 35).

Parity of 253

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

Find out more:

What is an even number?

Is 253 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 253 is about 15.906.

Thus, the square root of 253 is not an integer, and therefore 253 is not a square number.

What is the square number of 253?

The square of a number (here 253) is the result of the product of this number (253) by itself (i.e., 253 × 253); the square of 253 is sometimes called "raising 253 to the power 2", or "253 squared".

The square of 253 is 64 009 because 253 × 253 = 253² = 64 009.

As a consequence, 253 is the square root of 64 009.

Number of digits of 253

253 is a number with 3 digits.

What are the multiples of 253?

The multiples of 253 are all integers evenly divisible by 253, that is all numbers such that the remainder of the division by 253 is zero. There are infinitely many multiples of 253. The smallest multiples of 253 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 253 too, since 0 × 253 = 0
253: indeed, 253 is a multiple of itself, since 253 is evenly divisible by 253 (we have 253 / 253 = 1, so the remainder of this division is indeed zero)
506: indeed, 506 = 253 × 2
759: indeed, 759 = 253 × 3
1 012: indeed, 1 012 = 253 × 4
1 265: indeed, 1 265 = 253 × 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 253). 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 15.906). 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 253

Preceding numbers: …251, 252
Following numbers: 254, 255…

Nearest numbers from 253

Preceding prime number: 251
Following prime number: 257