Is 264 a prime number?

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

For 264, the answer is: No, 264 is not a prime number.

The list of all positive divisors (i.e., the list of all integers that divide 264) is as follows: 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264.

For 264 to be a prime number, it would have been required that 264 has only two divisors, i.e., itself and 1.

Find out more:

What is a prime number?

As a consequence:

264 is a multiple of 1
264 is a multiple of 2
264 is a multiple of 3
264 is a multiple of 4
264 is a multiple of 6
264 is a multiple of 8
264 is a multiple of 11
264 is a multiple of 12
264 is a multiple of 22
264 is a multiple of 24
264 is a multiple of 33
264 is a multiple of 44
264 is a multiple of 66
264 is a multiple of 88
264 is a multiple of 132

For 264 to be a prime number, it would have been required that 264 has only two divisors, i.e., itself and 1.

Is 264 a deficient number?

No, 264 is not a deficient number: to be deficient, 264 should have been such that 264 is larger than the sum of its proper divisors, i.e., the divisors of 264 without 264 itself (that is 1 + 2 + 3 + 4 + 6 + 8 + 11 + 12 + 22 + 24 + 33 + 44 + 66 + 88 + 132 = 456).

In fact, 264 is an abundant number; 264 is strictly smaller than the sum of its proper divisors (that is 1 + 2 + 3 + 4 + 6 + 8 + 11 + 12 + 22 + 24 + 33 + 44 + 66 + 88 + 132 = 456). The smallest abundant number is 12.

Parity of 264

264 is an even number, because it is evenly divisible by 2: 264 / 2 = 132.

Find out more:

What is an even number?

Is 264 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 264 is about 16.248.

Thus, the square root of 264 is not an integer, and therefore 264 is not a square number.

What is the square number of 264?

The square of a number (here 264) is the result of the product of this number (264) by itself (i.e., 264 × 264); the square of 264 is sometimes called "raising 264 to the power 2", or "264 squared".

The square of 264 is 69 696 because 264 × 264 = 264² = 69 696.

As a consequence, 264 is the square root of 69 696.

Number of digits of 264

264 is a number with 3 digits.

What are the multiples of 264?

The multiples of 264 are all integers evenly divisible by 264, that is all numbers such that the remainder of the division by 264 is zero. There are infinitely many multiples of 264. The smallest multiples of 264 are:

0: indeed, 0 is divisible by any natural number, and it is thus a multiple of 264 too, since 0 × 264 = 0
264: indeed, 264 is a multiple of itself, since 264 is evenly divisible by 264 (we have 264 / 264 = 1, so the remainder of this division is indeed zero)
528: indeed, 528 = 264 × 2
792: indeed, 792 = 264 × 3
1 056: indeed, 1 056 = 264 × 4
1 320: indeed, 1 320 = 264 × 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 264). 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 16.248). 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 264

Preceding numbers: …262, 263
Following numbers: 265, 266…

Nearest numbers from 264

Preceding prime number: 263
Following prime number: 269